LOGICAL REASONI ONING SYLL YLLOGI OGIS SM Predicate : Predicate is the part of the proposition denoting that which which is affirmed affi rmed or denied about the subject.
The word "syllogism" "syllogism" is given by Greeks which means 'inference' or 'deduction'. It was introduced by Aristotle.
ii)
An example of a question of syllogism syllogism is given below. below.
eg : In the the prop propos osit itio ion n All novels are songs, something is being said about novels. So novels. So novels is the subject. Songs is the predicate here because it affirmed about the subject.
Directions : : In the following questions, two statements are given followed by two conclusions. You have to study the two statements and then decide which of the conclusions follow from the statements.
CLASSIFICATION OF PROPOSITIONS i)
Mark the right answer from (1), (2), (3), (3 ), (4) and (5) Stat Statem emen ents ts :
All All pla plant nts s are are tree trees s. No trees are green.
Conclusions :
eg : All girls are disciplined.
I. Some plan lants are green. II. No plant plants s are are green green..
1)
Only I follows
2)
Only II follows
3)
Both I and II follow
4)
Either I or II follo llows
5)
Neith ither I nor II follow lows
This is a typical question of syllogism. Here Her e the th e choice c hoice (2) is true. La Later ter on we we can discuss the method to reach at a t the answer choice. Now let us see some some definitions definitio ns related to syllogism.
All bulbs are lions. i)
No boxes are baskets. ii)
Some boys are cats. iv)
Some fans are not black.
ii) ii) No cloth cloth is a bay bay iv) Some green green are not white white The parts of proposition are giv en below. i)
Subject : A su subje bject is the the pa part of th the proposition about which something is being said.
Particu Particu lar negative prop osit ion : A proposition proposition of the form Some S are not P is called particular negative proposition. It is denoted by the letter O. eg : Some flowers are not grapes.
i) All All wind indows are rods iii) Some studen students ts are are members members
Particular Particular positive Propositio Propositio n : A proposition of the form Some S are P is P is called a particular positive proposition. proposition. It is usually denoted by I. eg : Some boys are smarts.
In logic, any statement is termed a proposition. Eg :
Universal Universal negative propo sitio n : A A proposition of the form No S is P is P is called a universal negative proposition. It is usually denoted by E. eg : No professors is l azy.
PROPOSITION A proposition is a sentence that makes a statement and giv es a relation between two or more terms.
Universal positi ve propo sition : A proposition of the form All form All S are P is P is called a universal positive proposition. A universal positive proposition is denoted by A.
In syllogism, syllogism, there are twotypes of inferences. inferences. 1)
Mediate ediate infere inference nce :
Here conclusion is drawn from two propositions. For example, if you are given All given All cats are dogs dogs and All and All dogs are animals, animals, then a conclusion of the form All form All cats are animals animals could could be drawn from it.
2)
Imme Immediat diate e infere inference nce :
A - ty pe hi dd en prop pr op os it io ns :
Here conclusion is drawn from only one given proposition. For example if a given statement is All is All gates are blue, blue, then based on this a conclusion could be drawn that Some blue are gates. gates. This is a case of immediate inference. Two important cases of immediate inference is given giv en below. below.
All All pos positive itive pro propos positio ition ns begin eginni ning ng with ith 'each', 'every' and 'any'. A po positive tive sente ntence with ith a particu icular lar person as its subject. A po positiv itive e se sentence wit with h a ver very de defin finite ite exception. eg : Each of them plays football.
a)
He should be awarded.
• •
Implic mplica ations tions :
If a given proposition is A - type, then it also implies that the I - type conclusion must be true. Let us verify it by considering the proposition, All proposition, All elepha elephants nts are big. big. This statement naturally implies that the conclusion Some elephants are big must big must be true. Similarly we can prove that an E - type proposition also implies an O - type conclusion. b)
•
Conve onverrsion sion
Two steps are to be followed foll owed in conversion. conversi on. The first step is to change the subject as the predicate and the predicate as the subject. The second step is to change the type of the given proposition to the pattern given in i n the following table. Type of the given pr proposition A
Type of the proposition after conversion I
E
E
I
I
O
Cannot be converted
Let us consider the statement Some posters are good looking. looking. This can be converted by using the above table as Some good looking are posters. posters. In the same way, No books are pencils can be converted as No pencils are books. books.
All members members except except Kavitha have a share share of profit. E - type hidden prop ositi on • • • •
eg : None can escape from death. Swathi is not an IAS officer. No student except Salim Sali m has attend the t he party. party. Is there any person who can can cheat himself? himself ? I - type type hidden propositions : •
Pos Positiv itive e pro propo pos sitio itions ns begin eginni nin ng wit with h wor word ds such as 'most', 'a few', 'mostly', 'generally', 'general ly', 'almost', `frequently', and negative propositions beginning with words such as 'few', 'seldom', `hardly', 'scarcely', 'rarely' and 'little'.
•
A po positiv itive e se sentence wit with h an an exc exce eptio tion which is not definite. eg : Very few writers research before they write. Seldom are people not jealous. All studen students ts except five have have failed.
HIDDEN PROPOSITION You may find it difficult diff icult to categorise some propositions of the form Rahim is brilliant, brilliant, Every man talks English, English, Not a single student passed the exam, exam, No student except Prem was present, present , etc. We shall know, how to find the hidden propositions in such sentences.
All negative ive se sentences be beginn inning ing wit with h 'no one', 'none' and 'not a single' A se sentence wit with h a partic ticular lar pe person as as its subject but a negativ e sense. A neg negativ ative e sent entenc ence with ith a very very defi defin nite ite exception. An inte interr rro ogati gative ve sente entenc nce e which hich is used to make an assertion.
O - type hidden prop ositi ons : •
All All neg nega ative tive pro propos positio itions ns begi begin nning ning with ith words such such as 'all', 'every', 'any' and 'each'. ' each'.
•
Negat egative ive prop propos osit itio ions ns with ith wo words rds as as 'mo 'mos st' , 'a few', 'mostly', 'generally', 'almost', and `frequently'.
•
•
Posi ti ti ve ve wo word s beg in inni ng ng wi wi th th 'f'f ew ew', 'seldom', 'hardly', scarcely', 'rarely' and little. A ne negative ive se sentence with ith an an exc exce eption ion which is not definite.. e.g. : All m en are not honest Most of the books have not been read. Girls are usually not brave. Rarely is a rich man worried.
eg :
All pins are hats. hats. In this pair, the common term is 'hat' and it is the predicate of both the sentences. So we have to align the sentences by converting any of the sentences and changing the order if needed. After alignment, the above example will will become All pins are hats
No students except a f ew are absent.
No hat is watch.
EXCLUSIVE PROPOSITIONS A statement statement beginning with'only', with'only', 'alone', 'none but' or 'none else but' is called exclusiv e proposition. Such propositions can be reduced to A or E or I type. Only brave men are pilots. pilots. This sentence means that "No coward man is a pilot" and "All pil ots are brave men". SOLUTION OF SYLLOGISM BY ANALYTICAL METHOD There are two steps to be followed for solving syllogism by analytical method. A problem of syll ogism consists of two propositions which have one common term. This common term will be the predicate of the first proposition and the subject of the second. If this condition is not satisfied in the given propositions, they should be aligned accordingl y.
Statements Statements : No watch is hat
While Whil e aligning a given pair of statements, the priority should be given while converting, to I - type statements to E-type E-t ype statements and then to A - type statement, in that order. That is, the rule of IEA should be f ollowed. After After aligning aligning the given pair of state statemen ments, ts, the conclusion can be easily drawn by using the following table. Sta Stateme tement nt - I A A E E I I
+ + + + + +
Stat State ement ment - II A = E = A = I = A = E =
Conc Conclu lusi sion on A E O* O* I O
No definite conclusion can be drawn for other combinations like A+I, O+ A etc, which are not mentioned in the above table.
eg : Statement : All birds birds are trees trees.. Some trees are cows. Here the common term is 'trees'. Also it satisfies the above said condition. Hence the statements are properly aligned.
For the above given combinations combination s which which are aligned properly, the conclusion is a proposition whose subject subject is the subject of the first statement and whose predicate is the predicate of the second statements. The common term s disappears.
Let us consider another example.
In the above table, O* implies that the conclusion is of type - O, whose subject subject is the predicate of the second statement and the predicate of the conclusion is the subject of the first statement.
eg : Statement : All penc pencils ils are are bott bottles les All bricks are pencils. Here the common term is 'pencil'. But it does not satisfy the given condition. So we have to align this pair. This can be aligned easily by changing the order of the statements. The aligned pair will be All bricks are pencils. All pencils are bottles.
SOLVED EXAMPLES. 1.
State tatem ments : All All bags are toys. All toys are keys.
The sentences are already aligned. From the above given Table, A+A=A. Hence the
conclusion is of type - A whose subject is the subject of the first proposition propositi on and the predicate is the predicate of the second proposition. So the conclusion is All is All bags are keys. keys. 2.
Now by changing the order of the statements, we can align the sentences. So the aligned pair is, No clip is red. Some red are caps.
State tateme ment nts s : All teachers are readers. All teachers are writers.
This pair is not properly ali gned because the subject of both the sentences is 'teachers'. Since both the sentences are of type - A, we may convert any of them. So the aligned pair is Some readers are teachers. All teachers are writers. Here the conclusion will be of type - I because because I+A=I. The conclusion is Some readers are
writers. 3.
State tateme ments nts : Some chocolates are toffees. All chocolates are pastries.
The subject of both the sentences is the same.By the rule of IEA, we convert the I - type statement. So the aligned pair is, Some toffees toff ees are chocolates. All chocolates are pastries pastries I+A=I. So the conclusion is Some toffees toff ees are pastries. 4.
State tateme ment nts s : All All lights are balls No bats are lights
By changing the order of the statements itself we can align the sentences. sentences. The aligned pair is is No bats are lights. All lights are balls. E+A=O*. So the conclusion is, Some balls are not bats. 5.
State tateme ments nts :Some caps are red. No clip is red.
Here the common term is 'red' which is the predicate of both the sentences. By the rule of IEA, we convert the I - type statement. After conversion, the given pair becomes, Some red are caps. No clip is red.
The conclusion is of type O* since E+I=O*. Hence the conclusion is Some caps are not clips. 6.
State tateme ments nts : Some powders are not soaps.
All soaps are detergents. The given pair i s properly aligned. But no definite conclusion can be drawn from this type because it is a O+A - type combination.
IMMEDIATE INFERENCE Now let us consider an example which has two statements as well well as two conclusi ons. eg. Statements: Statements : All novels are storie stories. s. All stories are songs. songs. Conclusion :
(i) All novels novels are are son songs. gs. (ii) (ii) Some songs songs are are novels.
First of all let us consider only the statements . The sentences are already ali gned. Since A+A = A, A , the conclusion will will be All be All novels are songs If we convert this conclusion, conclusion, we get get Some songs are novels.Hence novels .Hence both the conclutions given in the question are true. Statements :Some roses are leaves. eg: Statements :Some Some leaves leav es are throns. Conclusions :
(i) Some rose roses s are thorn thorns. s. (II) (II) Some leaves are roses. roses.
We know that for a combination of I+I type no conclusion could be drawn. But if we convert the fi rst statement, we get Some leaves are roses. roses. Which Whi ch is conclusion (ii) (ii) Also on converting the second statement, we get some thorns are leaves. leaves. This proposition proposition is not not given in the conclusion part. So in this example, conclusion (ii) alone is true. So while solving the problems on syllogism, we should also take the immediate inferences of the given statements as well as the immediate inference inf erence of the conclusion drawn drawn from the table.
COMPLEMENTARY PAIR Consider the following. Conclusions :i Conclusions :i)) Some buse buses s are are trucks. trucks. ii) Some Some buse buses s are are not not truc trucks ks.. We know that either some buses will be trucks or some buses will not be trucks. Hence either (i) or (ii) i s true. Such pair of statements are called complementary pairs. So in a complementary pair, at least one of the two statements is always true. We can call a pair as a complementary pair if i) ii)
The They are are an I + O - type type pair pair or an A + O type pair or an I + E - type pair.
below. All birds are swans .
i i i)
State tatem ments : Some cows are horses All cows are are tigers.
Conclusions :
i) Some Some tige tigers rs are are hors horses es..
ii) ii) Some tigers tigers are cows. cows. To align the sentences, it i s sufficient to convert the fi rst statement. So the aligned pair is Some horses are cows. All cows are tigers. I + A = I. Hence the conclusion will be Some horses are tigers. tigers. If we convert this conclusion, we get Some tigers are horses which horses which is conclusion (i). Also if we convert the second statement, conclusion (ii) is obtained.
Some tables are not watches.
Hence both the conclusions given above should be taken as true. There is no need to check for complementary pair because definite conclusion has already been obtained.
Some girls irls are cute.
3.
Some birds bi rds are not swans. ii)
2.
The The subje ubject ct and and pre predi dica cate te of both both the the sentences are the same.
Some complementary pairs are given i)
I + E = O. So the conclusion is Some houses are not stones, stones, Hence we obtain a definite conclusion that conclusion (ii) is correct. Hence step IV becomes unnecessary.
Some tab tables les are watches.
No girls are cute. Note : The steps to be followed to do a syllogism problem by analytical method are mentioned below. i)
Alig lign the sentences properly
ii)
Draw raw con conclus clusio ion n us using ing the the tabl table e
iii) iii)
Check heck for for imm immed edia iate te infe infere ren nces. ces.
iv)
Chec Check k for for com compl plem emen enta tary ry pair pair ifif ste steps ps ii and iii fail.
SOLVED EXAMPLES 1. Statement : No rooms rooms are stones Some houses are rooms. Conclusions :
i) Some Some hou house ses s are are ston stones es ii) Somehouse houses s are are not stones stones..
We can easily align the statements by changing the order of the sentences. The aligned ali gned pair is : Some houses are rooms. No rooms are stones.
State tatem ments : Some poets are teachers. Some teachers are saints
Conclusions :
i) Some Some poe poets ts are are saint saints. s. ii) Some poets poets are not saints saints..
This pair is already aligned. But there is no definite conclusion for f or I + I type combinations. combinati ons. Also Al so none of the giv en conclusi conc lusi ons is the immediate immedi ate inference of any of the statements. So let us check for the complementary pair. The conclusions given are in the form of 'some' and 'some not'. Hence either conclusion (i) or (ii) follows.
THREE - STATEMENT SYLLOGISM This type of syllogism problems consist of 3 statements which are followed by 4 or more conclusions. A typical typica l three - statement statemen t syllogism syll ogism problem is given giv en below. below. Directions : Below : Below are given three statements followed by several conclusions based on them. t hem. Examine the conclusions and decide whether
they logically follow from the given statements. You have to take the given statements as true even if they appear to be at variance with commonly known facts. Statements Statements :
A) All bags are hats.
and the subject of the third sentence are the same. iii) iii)
Now Now arri arrive ve at at the the conc conclu lus sion ion us using ing the the table.
iv)
Now Now com compa pare re the the give given n con concl clus usio ion n wit with h the conclusion drawn using the tables. If they match, the given conclusion is true. If they do not match, it i s false.
B) Some pins pins are are bags. bags. C) No hats hats are are needles. needles. Conclusions :
I) Some Some pins pins are are hat hats. s. II) No needle needles s are bags bags.. III) Some pins are needles. needles.
Step III i)
If a give given n state tateme ment nt has has alr alread eady been been marked as a valid concl usion after step II, then leave it. Otherwise check if it is an immediate inference of any of the three given statements of the conclusion derived.
ii)
Sear Searc ch fo for comp comple leme men ntar tary pai pairr :
IV) Some pins are not n needles eedles.. (a) (a) Only I and and II follow (b) (b) Only I and IV follow (c) (c) I, II and and IV follow follow (d) (d) Either III or IV, IV, and I follow (e) (e) Either III or IV and I and II follow. follow. Before solving this example, let us see the steps in solving a three-statement syllogi sm problems. Step I
a) Check Check if any two two given conclus conclusions ions have the same subject and the same predicate. b) If (a) is satisfied, then check check whether whether any of them has been marked as a valid conclusion after step II or as an immediate imm ediate inference.
i)
Conside ider a giv give en conclus lusion ion.
ii) ii)
Note ote the the su subjec bjectt and and pr predic edicat ate e of of this this give given n conclusion.
c) If none none of them them has been been marke marked d as a valid conclusion, then they will form a complementary pair if they are an A - O or I - O or I - E pair.
i i i)
N ow ow f i nd nd wh wh ic i c h o f t he he tw tw o gi gi v en en statements has this subject and predicate.
d) If they do make a complementa complementary ry pair pair,, then mark the choice "either of the two follows".
iv) a) If there there is a common common term term betw between een the two statements chosen in the previous part, then consider only these two statements.
If a conclusion is marked as a valid conclusion after step II, t hen it is not necessary necessary to perform step III (i). Again if a given giv en conclusion has already been accepted in step III (i), then it is not necessary to perform step III (ii ).
b) If there there is no no common term betwee between n the two statements chosen in the previous part, then we should consider all the three statements. Step II i) ii)
If two two st statem ateme ents nts ar are re releva levan nt fo for a give given n conclusion, align them. If thre three e state tatemen ments ts are are rele relevan vant, t, write write them them as a chain. That is, align them in such a way that the predicate of the first sentence and subject of the second are the same, and the predicate of the second sentence
The learner should understand these steps clearly. Now follow the solution to the example which is already giv en. Here we have to check the validity of each and every conclusions one by one. Conclusion I : Here the subject is pin and the t he predicate is hat. So let us consider (A) and (B) as our relevant statements because they have a common term 'bags'. The second step is to align the sentences. The aligned pair is,
Some pins are bags. All bags are hats. I + A = I. So we arrive at the conclusion, 'Some pins are hats'. So conclusion I is val id. Conclusion II : Here the subject is 'needles' and the predicate is 'bags'. Statement C contains the subject 'Needles'. But 'bags' appears in both A and B. We should should select A because because there there is a common term between A and C. This is an aligned pair and so we arrive at the conclusion No bags are needles needles which which implies No needles are bags. bags. Hence conclusion II is valid. Conclusio n III : Here the subject is 'pins' and the 'predicate' i s needles. These words appear in statements (B) and (C) respectively which have no term in common. So all the t he three statements should be taken as relevant. Now align the stat stateme ement nts s as as Step Step II II (ii) (ii) So we get, get, Some pins are bags All bags are hats. No hats are needles. I + A + E = (I + A) + E= I + E = O. So the conclusion is 'Some pins are not needles', which is conclusion conclu sion IV. So conclusion conclusio n IV is valid. Since conclusion III is not vali d in step II, let us perform step III (i). The conclusion, concl usion, Some pins are not needles needles is not an immediate inference of any of the three given statements. statements. So the next step is to check the existence of a complementary pair in the giv en conclusions. conclusions. We see that conclusion III and conclusion IV form a complem entary pair of I - O type. So the choice "either III or IV follows" could be selected. But we find that conclusion IV is vali d from the previ ous step. So conclusion III is not valid. Hence for this given example, the third choice which is 'I, II and IV foll ow' is true.
PRACTICE TEST Directi on s (Qs. 1 - 25) 25) : Each of the following questions contains two statements followed by two conclusions conclus ions numbered I and II. You have to consider the two statements to be true, even if they seen to be at variance at the commonly known facts. You have to decide which of the
given conclusions definitely follows from the given statements. Give answer ((a) if only I follows ; ((b) if only conclusion II follows ; ((c) if either I or II follows; ((d) if neither I nor II follows and ((e) if both I and II follow. 1. Statement Statement : Some tables are glasses. All trees are are tables. Conclusions: I.Some trees are glasses II. Some glasses gl asses are trees. trees. 2.
Statement Statement :
No man is a lion. Somu is a man. Conclusions: I. Somu is not a lion. II. All men m en are not Somu. 3. Statement Statement : All boys are mothers. All mothers are fathers. Conclusions : I. All mothers are boys. II. All boys are fathers. 4. Statement Statement : All pots are cups. All cups are bowls. bowls. Conclusions: I. All pots are bowls. II. All cups are pots. 5. Statement Statement : All students are girls. No girl is dull Conclusions : I. There are no boys in the class II. No student is dull. 6. Statement Statement : Some cats are kittens. All goats are kittens. Conclusions: Conclusions: I. Some Some cat cats s are are goa goats ts.. II. Some goats are cats. 7. Statement : All All nam names es are are hous houses es.. No houses are foxes. Conclusions : Conclusions : I. All names names are are foxes foxes.. II. No houses are names. 8. Statement : All All pen pens s are are dogs ogs. Some pens are lights. Conclusions: Conclusions: I. Some Some dogs dogs are are light lights. s. II. Some li ghts are not dogs 9. Statement : Some Some bird birds s are are clou clouds ds.. Horse is a bird. Conclusions : I. Some Some clouds clouds are are birds. birds. II. Horse is not a cloud. 10. Statement : All All ta table bles are ants ants.. Some ants are chairs. Conclusions: Conclusions: I. All ant ants s are are tab tables les.. II. Some chairs c hairs are not ants. 11. Statement : All All elep elepha hant nts s are are bird birds. s. Some birds bi rds are cows.
Conclusions: Conclusions: I. Some Some cow cows are are birds birds..
II.Some elephants are cows. Statemen t : 12. 12. Statement Conclusions: Conclusions:
13. Statement : Conclusions: Conclusions:
14. Statement : Conclusions: Conclusions: 15. Statement : Conclusions: Conclusions: 16. Statement : Conclusions: Conclusions: 17. Statement : Conclusions: Conclusions:
18. Statement : Conclusions: Conclusions:
19. Statement : Conclusions: Conclusions: 20. Statement : Conclusions: Conclusions: 21. Statement : Conclusions: Conclusions: 22. Statement : Conclusions: Conclusions:
All papers are pencils ils. All pencils are erasers. I.Som I.Some e eras erases es are are paper papers. s. II. Some pencils are not papers. Some Some tree trees s are are hors horses es.. Some ships are trees. I.So I.Some me hor horse ses s are are ship ships. s. II.Some trees are neither ships nor horses. All All glas glass ses are are mirr mirror ors s. Some mirrors are red. I. All All mirro mirrors rs are are glas glasse ses. s. II. Some glasses are red. Some Some dogs dogs are are hors horses es.. No horse is black. I. Some Some dog dogs s are are black. black. II.Some II.Som e horses are dogs. All All roa roads ds are are pol poles es.. No poles are houses. I. Some roads roads are are hou house ses. s. II.Some houses are poles. Many Many act actor ors s are are singe ingers rs.. All singers are dancers. I. Some Some acto actors rs are are dancers. II. No singer is an actor. Only Only cat cats s are are anim animal als s. No historian is an animal. I. Some Some cats cats are are not not historians. II. Some historians are not cats. Some Some desks esks are are cap caps s. No cap is red. I. Some Some caps caps are are des desks ks.. II. No desk is red. Some Some pots ots are are belt belts s. No belt is white. I. Some Some pot pots s are are whit white. e. II. Some pots are not white. Some Some girl girls s are are flow flowe ers. rs. Some flowers fl owers are books. I. Some Some girl girls s are are boo books ks.. II. No books are girls. Some Some file files s are are ants ants.. All insects are ants. I. All All files files are are ant ants s. II. Some ants are insects.
23. Statement :
All All pla playe yerrs are tall tall.. Pranesh is tall. Conclusions: Conclusions: I. Pra Prane nesh sh is a playe playerr. II. Pranesh is not a player. 24. Statement : Some Some hens ens ar are co cows. All cows are horses. Conclusions : Conclusions : I. Some hors horses es are are hens. hens. II. Some hens are horses. 25. Statement : All All bus busin ines ess s men men are are har hard d working. No hard working men are superstitious. Conclusions: Conclusions: I. No No busi busine ness ss men are are superstitious. II. All superstitious are not businessmen. Directio ns (Qs. 26 - 40) 40) : In : In each question below, there are two or three statements followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follow(s) from the given statements. 26. Statements: Some boys are girls. All girls are students. students. Conclusions: I. Some Some boys boys are are stu stude dent nts. s. II. Some studen students ts are boys. boys. III. III. Some students students are are girls. IV. IV. All students are are girls. (a) (a) I, II and and III follow (b) (b) II, III and IV follow (c) (c) I, III and and IV follow (d) (d) I, II and IV follow (e) (e) All follow 27. Statements: All Statements: All books are watches. Some watches are clips. Conclusions: I. Some Some watche ches ar are books. II. No watc watches hes are books books.. III. III. Some books are clips. IV. IV. No books are are clips. (a) (a) I,and III III follow (b) (b) Only I follow follow (c) (c) Either I or II II follows (d) (d) Either III or IV and I follow (e) (e) Either I or II and III follow. follow. Statements : Some chairs are tables. 28. Statements: tables. Some tables are desks.
Conclusions: I. Some Some chai chairs rs are desk desks. s. II. No chair chairs s are are desk desks. s. III. III. Only desks are chairs. chairs. IV. IV. Only chairs are desks. desks. (a) (a) Only I follows follows (b) (b) Only II follows follows (c) (c) Either I or II II follows. follows. (d) (d) Either III or IV follows (e) (e) Either I or II and either III or IV follow. 29. Statements: Statements : Some reds reds are blues. No greens are blues. Conclusions : I. Some Some reds reds are are not not green greens. s. II. All reds reds are greens greens.. III. III. Some greens are not reds. reds. IV. IV. All greens are reds. (a) (a) Only I follows follows (b) (b) Only III follows follows (c) (c) Either I or II II follows. follows. (d) (d) Either III III or IV and I follow (e) (e) I and II follow. 30. Statements :No systems are decks. All decks are books. Conclusions: Conclusions: I. Some Some sys syste tems ms are are book books. s. II. Some syst systems ems are are not books books.. III. III. Some books are systems. systems. IV. IV. Some books are not systems. systems. (a) (a) Only II follows follows (b) (b) Only IV follows follows (c) (c) I and IV follow. follow. (d) (d) II and either III or or IV follow (e) (e) Either I or II and IV follow. 31. Statements :All Statements :All birds are animals. Many birds are stones. Conclusions : I. Some Some bird birds s are are anima animals ls.. II. Some animal animals s are stones stones.. III. III. All animals are stones. stones. IV. IV. Some animals are not stones. stones. (a) (a) Only I follows follows (b) (b) Only II follows follows (c) (c) Either III III or IV follows. follows. (d) (d) I and II follow follow (e) (e) I and II and either III or IV follow 32. Statements Statements : Some teachers are students. Some students are boys.
33.
34.
35.
36.
Conclusions: I. All boy boys s are are stud student ents. s. II. All boys boys are teacher teachers. s. III. III. Some teachers teachers are boys. boys. IV. IV. No teachers teachers are boys. (a) (a) Only I follows follows (b) (b) Only II and and II follow (c) (c) Either I or or III follows follows (d) (d) Either I or IV IV follows (e) (e) Either III or or IV follows Statements: Statements : Some girls are teens. teens. No teens are snakes. Conclusions : I. Some Some tee teens ns are are girl girls s. II. Some snake snakes s are are no girls. girls. III. III. Some girls are not snakes. snakes. IV. IV. All snakes are girls. (a) (a) Only I follows follows (b) (b) Either II or or III follows (c) (c) Only I and and III III follow (d) (d) Only I and II follow (e) (e) Either III or or IV follows Statements :No Statements :No blankets are pill ows. Some beds are blankets. Conclusions : I. Some Some blank blanket ets s are are not pillo pillows ws.. II. Some pillow pillows s are not beds. beds. III. III. Some beds are not not pillows. IV. IV. All beds are pillows. pillows. (a) (a) Either III or or IV follows (b) (b) Either I or II follows follows (c) I and and III III follow (d) (d) Either II or or III follows (e) (e) None of the above Statements: Statements : All classes are are glasses. glasses. All brasses are glasses. Conclusions : I. Some Some class classes es are are bras brasse ses. s. II. Some brass brasses es are glass glasses es.. III. III. Some brasses brasses are classes. classes. IV. IV. Some classes are glasses. (a) (a) Only I follows follows (b) (b) Only II follows follows (c) (c) I and and II follow follow (d) (d) II and and IV follow (e) All follow follow Statements: Statements : All cars are are buses. buses. Some buses are cycles. Conclusions: Conclusions: I. All All cycles cycles are are buse buses. s. II. All cycle cycles s are are car. car.
37.
38.
39.
40.
III. III. Some cars are cycles. cycles. IV. IV. No cars are cycles. cycles. (a) (a) Only I follows follows (b) (b) Only II and and III follow (c) Either II or or III follows (d) (d) Either I or IV IV follows (e) (e) Either III or IV follows Statements: Statements : Some singers are rockers. rockers. All rockers rockers are westerner westerners. s. Conclusions: Conclusions: I. Some Some rocke rockers rs are are sing singers ers.. II. Some weste westerners rners are rockers. rockers. III. III. Some singers are westerner westerners. s. IV. IV. Some singers singers are not westerners. (a) (a) I, II and III III follow (b) (b) I, II and IV follow (c) (c) II, III III and IV follow follow (d) (d) I, III and IV follow (e) All follow follow Statements: Statements : All pigs are are elephants. elephants. No pigs are bakers. Conclusions : I. Some Some baker bakers s are not pigs. pigs. II. Some pigs pigs are not not bakers bakers.. III. III. Some elephant elephant are not bakers. bakers. IV. IV. Some bakers are not elephants elephants (a) (a) I, II and III III follow (b) (b) I, II and IV follow (c) (c) I, III and and IV follow follow (d) (d) II, III and IV follow (e) All follow follow Statements : Statements : All green are blue. blue. All blue are white. Conclusions : I. Some Some blue blue are are gre green en.. II. Some white white are are green green.. III. III. Some green are are not white. white. IV. IV. All white are are blue. (a) (a) Only I and II follow (b) (b) Only II and and III follow (c) (c) Only I and and III follow follow (d) (d) Only I and IV follow (e) All follow follow Statements: Statements : Some soaps soaps are are clean. All clean are wet. wet. Conclusions : I. Some Some clea clean n are soaps soaps.. II. No clean are soaps soaps.. III. III. Some wet are are soaps. soaps. IV. IV. All wet are soaps. soaps.
(a) (a) Only I follows follows (b) (b) Either I or II follows (c) Either III or IV follows (d) (d) Only I and and III follow (e) (e) None of of the above Directio ns (Qs. 41 - 60) 60) : Below are given three statements A, B,and C followed by four conclusions. You have to take the given statements to be true even if they appear to be at variance with commonly known facts, and then decide which of the conclusions logically follow (s) from the given statements. F or each question, mark out an appropriate answer choice that you think is correct. 41. Statements: Statements : A. All thieves are men. B. All men are are gradua graduates tes.. C. No graduates graduates are are employed. employed. Conclusions : I. Some Some grad graduat uates es are thieves thieves.. II. No employed employed are thieves. thieves. III. III. Some men are are thieves. thieves. IV. IV. Some employed are men. (a) (a) I, II and and III follow (b) (b) II, III and IV follow (c) (c) Only I and II follow (d) (d) Only II and and II follow (e) (e) Only II and IV follow. follow. 42. Statements: A. Some books are pens B. All tables tables are chairs chairs.. C. No pens pens are tables. Conclusions: I. Some Some books books are not not table tables. s. II. Some pens pens are not not chairs chairs.. III. III. Some books are are not chairs. chairs. IV. IV. Some chairs are not not pens (a) (a) I, and IV IV follow (b) (b) II, and IV follow (c) I and and III follow (d) (d) II and III III follow (e) (e) III, and IV follow. follow. 43. Statements Statements : A. All satelli tes are planets. B. No stars stars are planets planets.. C. Some cosmos cosmos are satellites. satellites. Conclusions: I. Some Some cosmo cosmos s are stars stars.. II. Some cosmo cosmos s are are planets planets..
III. III. Some stars are not cosmos. cosmos. IV. IV. Some cosmos are not stars stars (a) (a) Only II and and III follow (b) (b) Only II and and IV follow (c) (c) Either I or or IV follows follows (d) (d) Only IV follows follows (e) (e) Either I or IV and and III follow 44. Statements: A. All books are notes. B. Some notes notes are penc pencils. ils. C. No pencils pencils are are papers papers.. Conclusions: I. Some Some note notes s are books books.. II. Some pencils pencils are books. books. III. III. Some books are papers. papers. IV. IV. No books are papers. papers. (a) (a) Only I follows follows (b) (b) Only I and either III or IV follows (c) (c) Either III III or IV follows follows (d) (d) Only I and and III follow (e) (e) None of these. these. 45. Statements : Statements : A. Some cups are utensils. B. No utensils utensils are are buckets buckets.. C. All buckets buckets are are plates. plates. Conclusions: I. Some Some cups cups are are buc bucket kets. s. II. Some utens utensils ils are are plates. plates. III. III. No utensils utensils are plates. plates. IV. IV. Some cups are plates plates (a) (a) Only I follows follows (b) (b) Only III follows follows (c) Either II or or III follows (d) (d) Either III or IV follows (e) (e) None of of these 46. Statements Statements : A. Some keys are locks. B. All locks locks are are doors doors.. C. Some doors doors are are windows windows.. Conclusions: I. Some Some locks locks are window windows. s. II. Some windo windows ws are keys. keys. III. III. Some windows windows are doors. doors. IV. IV. No locks windows. (a) (a) Either I or IV IV follows (b) (b) Only II follows follows (c) (c) Only III and IV IV follow (d) (d) None follows (e) (e) None of these. these.
47. Statements: A. All pins are staplers. B. Some staplers staplers are sharpen sharpeners ers.. C. Some sharpene sharpeners rs are are stands. stands. Conclusions: I. Some Some stap stapler lers s are are sta stands nds.. II. Some sharp sharpener eners s are pins pins.. III. III. Some pins are are stands. stands. IV. IV. Some stands are sharpeners. sharpeners. (a) (a) Only I and II follow (b) (b) Only II and and IV follow (c) (c) Only III III follows follows (d) (d) Only IV follows follows (e) (e) None of of these 48. Statements: A. Some oranges oranges are apples. B. All apples apples are guavas. guavas. C. No guavas guavas are banan bananas. as. Conclusions: I. Some Some gua guavas vas are oran orange ges. s. II. No apples apples are are banana bananas. s. III. III. Some oranges oranges are bananas. bananas. IV. IV. Some apples are bananas. bananas. (a) (a) Only I and II follow (b) (b) Only I and either either II or IV follow (c) (c) Only I, II and and IV follow (d) (d) Only III and either II or IV follow. (e) (e) None of of these 49. Statements: A. Some streets are roads. B. Some roads roads are lanes lanes.. C. Some lanes lanes are highways. highways. Conclusions : I. Some Some roads roads are are not str street eets. s. II. No highwa highways ys are are streets streets.. III. III. Some streets streets are not roads. roads. IV. IV. Some lanes are not roads. roads. (a) (a) Only III follows follows (b) (b) Only III and and IV follows (c) (c) Either I or or III follows follows (d) (d) Both I and and III follow (e) (e) None of of these 50. Statements Statements : A. Some pencils are pens. B. All pens pens are eras erasers ers.. C. All staplers staplers are are erasers erasers.. Conclusions: I. Some Some pens pens are are not not penc pencils ils.. II All eras eraser ers s are are pencils pencils.. III. III. Some staplers staplers are pens. pens. IV. IV. Some staplers are are pencils.
(a) (a) Only I follows follows (b) (b) Only II follows follows (c) (c) Only III III follows follows (d) (d) Only IV follows follows (e) (e) None follows 51. Statements: A. Some tables are are chairs. chairs. B. No cupboa cupboards rds are tables. tables. C. Some chairs chairs are are cupboard cupboards. s. Conclusions : I. Some Some chair chairs s are are not not table tables. s. II. All chairs chairs are are either either tables tables or cupboard cupboards. s. III. III. Some chairs chairs are are both both tables and cup boards IV. IV. All chairs are tables. tables. (a) (a) Only either I or IV follows. follows. (b) (b) Only either II or or III follows. (c) (c) Only IV follows. follows. (d) (d) Either II II or III and I follow (e) (e) None of these. these. 52. Statements Statements : A. All birds are are animals. B. Some animals animals are humans. humans. C. All humans humans are are mammals. mammals. Conclusions : I. Some Some huma humans ns are not birds birds.. II. Some birds birds are humans humans.. III. III. Some animals are not mammals. IV. IV. All animals are are mammals. (a) (a) Only I and II follow. follow. (b) (b) Either III or IV follows (c) (c) Either I or II II follows. follows. (d) (d) Either I or II and either III or IV follow (e) (e) None of these. these. 53. Statements Statements : A. Some leaves are fruits. B. All branch branches es are are fruits fruits . C. Some roots roots are branches branches.. Conclusions : I. Some Some roo roots ts are are fru fruits its.. II. Some branches branches are leaves. III. III. No leaves are branches. branches. IV. IV. Some leaves are roots. (a) (a) Either II or III and and I follow. follow. (b) (b) Only I follows follows (c) (c) Only either either II or III follows follows (d) (d) Only I and and III follow (e) (e) None of these. these.
54.
55.
56.
57.
Statements Statements : A. Some keys are locks. B. Some locks locks are are stickers stickers.. C. All stickers stickers are are pens. pens. Conclusions : I Some Some pens pens are are loc locks ks.. II Some Some stick stickers ers are keys. keys. III. III. No stickers are keys. IV. IV. Some locks are keys. keys. (a) (a) I, IV and and either II II or III III follow (b) (b) Only I and IV follow. (c) Only II and III follow. follow. (e) (e) None of these. these. Statements Statements : A. All books are papers. B. Some papers papers are journals. journals. C. Some journals journals are are calendars. calendars. Conclusions : I. Some Some jour journa nals ls are are boo books ks.. II. Some calendars calendars are papers. papers. III. III. Some books are journals. journals. IV. IV. Some books are calendars. calendars. (a) (a) Only II and and IV follow (b) (b) Only II and and III follow (c) (c) Only I and III III follow (d) (d) Only III and and IV follow (e) (e) None follows. Statements Statements : A. Some answers answers are questions. B. Some questions questions are writers. writers. C. All writers writers are poets poets.. Conclusions : I Some Some writ writer ers s are are ans answers ers. II. Some poets poets are questi questions ons.. III. III. All questions are are poets. IV. IV. Some poets are answers. answers. (a) (a) Only I and II follow follow (b) (b) Only I, II and IV IV follow (c) (c) Only II follows follows (d) (d) Only II and and IV follow (e) (e) Only III follows. follows. Statements Statements : A All bottles bottl es are boxes. B. All boxes boxes are bags bags.. C. Some bags bags are are trays. trays. Conclusions : I Some Some bott bottle les s are are tray trays. s. II Some Some tray trays s are boxes boxes.. III. III. All bottles are bags. bags. IV. IV. Some trays are bags. bags.
58.
59.
(a) (a) Only I, III and IV follow. (b) (b) Only II and III follow. follow. (c) Only I, II and and III follow. follow. (d) (d) Only III and IV follow. follow. (e) (e) All follow. follow. Statements Statements : A. Some envelops are gums. B. All gums gums are are seals seals.. C. Some seals seals are adhes adhesives. ives. Conclusion onclusion : I Some Some enve envelo lops ps are sea seals ls.. II. Some gums are adhesives adhesives.. III. III. Some adhesives adhesives are seals. seals. IV. IV. Some adhersives adhersives are gums. gums. (a) (a) Only I and II follow (b) (b) Only I and and III follow (c) (c) Only II and and IV follow (d) (d) Only III and and IV follow (e) (e) Only I and IV follow. Statements Statements : A. All flowers are garlands. B. All garland garlands s are are fruits. fruits. C. All fruits fruits are trees. trees.
60.
Conclusions : I. All tre trees es are flowe flowers rs.. II. Not all all trees trees are are flowers flowers.. (a) (a) Only I follows follows (b) (b) Only II follows follows (c) (c) Either I nor nor II follows follows (d) (d) Neither I or II follows. (e) (e) Both I and and II follow. follow. Statements Statements : A. All chairs are apples. B. Some apples apples are tables tables.. C. All tables are are cupboard cupboards. s. Conclusions : I. Some Some cupb cupboa oards rds are are chairs chairs.. II. Some tables tables are not not chairs chairs.. (a) (a) Only I follows follows (b) (b) Only II follows. follows. (c) (c) Either I or II follows (d) (d) Neither I nor II follows (e) (e) Both I and II follows. follows.
ANSWERS AND EXPLANATIONS 1.
(4)
2.
(a )
9.
(a (a)
1 0 . (d)
1 7 . (a)
3.
(b)
4.
(a)
5 . (e)
6.
1 1 . (a )
1 2 . (a)
13. (d)
1 4 . (d)
1 5 . (b)
16 .( d)
1 8 . (a )
1 9 . (a )
2 0 . (b)
2 1 . ( c)
2 2 . (b)
2 3 . (c)
2 4 . (e )
2 5 . (e)
26. (a)
27. (d)
2 8 . (c)
29. (d)
3 0. (e)
3 1 . (e)
3 2 . (e )
3 3 . (c)
3 4 . (c )
3 5 . (d)
3 6 . (e)
3 7 . (a)
3 8 . (a)
3 9 . (a)
4 0 . (d)
4 1 . (a)
4 2 . (a )
4 3 . (b)
4 4 . (b)
4 5 . (c)
4 6 . (e)
4 7 . (d)
4 8 . (a )
4 9 . (e)
5 0 . (e )
5 1 . (a )
5 2 . (d)
5 3 . (a)
5 4 . (a)
5 5 . (e)
5 6 . (c )
5 7 . (d)
5 8 . (b)
5 9 . (b)
6 0 . (d)
1. d. d. The The alig aligne ned d pair pair is All trees are are tables Some tables are glasses. This is a `A + I - type pair which has no solution 2. a. a. Alig Align n thi this s pai pairr as as Somu is a man and man and No man is a lion. lion. A + E = E. So the conclusion is Somu is not a lion : lion : foll ows I follows 3. b. A + A = A. The The conc conclus lusion ion is All is All boys are fathers . fathers . II follows
(d)
7.
(d)
8.( a)
5. e. e. A + E = E. E. The The conc conclus lusion ion is No student is dull. dull. II follows. Since All Since All students' students' are girls, girls, which means No boys are students.' Hence I also f ollows. 6. d. Align Align this this pair pair as All as All goats are kittens and Some kittens are goats. goats. A + I pair pair has no definite conclusion. A + E = E, the the con conclu clusi sion on here here is No names are foxes. foxes. But this conclusion is not given. 8. a. a. The align aligned ed pair pair is Some lights are pens and All and All pens are dogs. dogs. So the conclusion
7. d.
is Some lights are dogs dogs which implies Some dogs are lights lights.. 9. a. The align aligned ed pair pair is is Horse is a bird and bird and Some birds are clouds. clouds. There is no definite conclusion for A + I - type pair. But conversion of statement I implies conclusion I. 10. d. A + I - type has no no definite conclusio conclusion. n. 11. a. a. A + I - type has no definite conclusion conclusion.. But immediate inference of Some birds are cows implies cows implies Some cows are birds birds.. Hence I follows. 12. a. The conclu conclusion sion is All is All papers are erasers erasers. Conclusion I follows from the immedi ate inference of this conclusion. 15. 15. b. I + E = O. So the conclusion conclusion is Some dogs are not black. black. But conclusion II follows as it is the conversion of the first statement. 16. 16. d. A + E = E. So the the conclusio conclusion n is No roads are houses. houses. 17. 17. a. I + A = I. So the conclusion conclusion is "Some actors are dancers". 18. 18. a. The first statement statement can can be converted converted to All animals are cats. cats. Now align the pair by changing the order as No historian is an animal. All animals are cats. E + A = O*. So the conclusion is Some cats are not historians. historians . 19. 19. a. I + E = O. So the conclusion conclusion is Some desks are not red. red. This is not given. But conclusion I is obvious from statement I. 20.b. 20.b. I + E = O. The conclus conclusion ion is Some pots are not white 21. c. I + I pair has no definite conclus conclusion. ion. But the choice make a complementary pair when we consider I and the immediate inference of II. Spot either I or II follows. 22. 22. b. The aligned aligned pair is All insects i nsects are ants. ants. Some ants are files. A + I - type pair pair has no definite solution. But conclusion II follows directly from statement II. 23. 23. c. Aligned pair is Pranesh is tall.
Some tall are players. A+ I - type pair has no definite definite conclusio conclusion. n. But Pranesh should either be a player or a non - player. Hence either of the two conclusions follows. 24. 24. e. I + A = I. So the the conclusion conclusion is Some hens are horses. horses . Again on conversion, this givesSome gives Some horses are hens. hens. 25. e. A +E = E. The conclusion is No businessmen are superstitious. superstitious. Also on conversion, conversion, this implies No superstitious are businessmen. businessmen. This implies Al l superstitious are not businessmen also businessmen also must be true. 26. 26. a. I + A = I. The conclusion conclusion is Some boys are students students which is I. This can be converted to Some students are boys, boys, which is II. Some students are girls follows girls follows from All from All girls girls are are students students.. 27. d. A+ I pair has no definite conclusion. But conclusion I follows directly from All books are watches. watches. III and IV are a complementary pair. 28. 28. c. I + I pair has no conclusion. But conclusion I and II form a complementary pair. Hence either I or II follows. foll ows. 29. 29. d. The aligned aligned pair is No greens are blues. Some blues are reds. E + I = O. So the conclusion is Some reds are not greens. greens. Hence I follows foll ows.. Also III and IV make a complementary compl ementary pair. 30. 30. e. e. E + A = O*. Hence the conclusion conclusion is Some books are not systems. systems . Again, I and II are a complementary pair. 31. e. Many birds are stones implies stones implies Some birds are stones. stones. The aligned pair is Some stones are birds. All birds are animals. I + A = I. Hence the conclusion is Some stones are animals. animals. On conversion conclusion II is obtained. I is obviously from statement I. Al so III and IV make a complementary pair. 32. 32. e. I + I - type pair has no conclus conclusion. ion. But III and IV are complementary complem entary pair. 33. 33. c. I + E = O. Hence Hence Some girls are not snakes follows. follows. Also I is obvious from the first statement.
34. 34. c. I + E = O. So the conclusio conclusion n is Some beds are not pillows. pillows. Hence III follows. Also I is obvious from the the first statement. statement. 35. 35. d. The aligned aligned pair is All classes are glasses. glasses. Some glasses gl asses are brasses. A + I - type pair pair has no solution. But II is obvious from All from All brasses brasses are glasses glassesand and IV is obvious from All from All classes classes are glasses glasses.. 38. 38. a. The aligned aligned pair is No backers are pigs. All pigs are elephants. E + A = O*. Hence the conclusion is Some elephants are not bakers. bakers. Thus III follows. No pigs are bakers implies that No bakers are pigs. pigs. I is obvious from this sentence. II follows directly from No pigs are bakers. bakers. Hence I, II and III fol low. low. 41. a. Conclusion drawn from statements A and B is All is All thieves thieves are graduate graduates s. Conclusion I is obvious from this sentence. III is obvious from statement A. Also A + A + E = A + E = E. Conclusion drawn drawn from all the three is No thieves are employed. employed. II is obvious from this sentence. 42. 42. a. I follows from statements statements A and C. IV foll ows from statements C and B. No other conclusion is possible 43. 43. b. Statements Statements C + A gives Some cosmos are planets. planets. So II is valid. By aligning II and B or by aligning all the three statements, we get IV. 44. 44. b. Conversion Conversion of A gives Some notes are books. Therefore I fol lows. For II A and B are the relevant releva nt statements. But A + I type pair has no conclusion. So II is not valid. For III all the statements are relevant. No definite conclusion can be obtained from this combination. But conclusions III and IV form a complementary pair.Hence either conclusion III or conclusion IV f ollows. 45. 45. c. For I, A and B are relevant. relevant. But the conclusion obtained here is Some cups are not buckets. buckets. So I is not valid. II and III form a complementary pair. For IV, IV, all the statements are relevant. But no conclusion is obtained for this combination.
46. 46. e. For I, B and and C are relevant. relevant. But here here no conclusion is obtained. Similarly Simila rly IV is not valid. valid . But I and IV form a complementary pair. So either I or IV follows. foll ows. For II all the three statements are relevant. relevant. But no conclusion follows from them. III is obvious obvi ous from C. Hence conclusions III and either I or IV follow foll ow.. 47. 47. d. For I, B and C are relevant. But no conclusion follows from them. For II all the three statements are relevant. But no conclusion follows follo ws from them. III also al so not valid vali d IV is obvious obvious from C. 48. 48. a. A + B gives Some oranges are guavas. guavas. I is obvious from this statement. B + C gives No apples are bananas. bananas. So II is valid. vali d. For III all the three statements are are relevant. But the conclusion arrived arriv ed here is Some oranges are not bananas. bananas. So III is invalid. IV is also invalid, inv alid, since II is valid. 49. 49. e. No conclusio conclusion n is derived derived from the given statements because I + I type pair has no solution. No conclusion can be arrived as the immediate inference of the statements. statements. There is no complementary pair also. So none follows. 50. 50. e. No conclusio conclusion n is derived derived form the given statements because (I + A) + I = I + I. This pair has no solution. Also no conclusion can be arrived as the immediate inference of the given statements and there is no complementary compl ementary pair. So none follows. 51. a. I and IV form a complementary complementary pair. pair. 52. d. I and II II form a complementa complementary ry pair pair and III III and IV form another complementary pair. 53. 53. a. C + B giv es I. Also Also II and III form a complementary pair. 54. 54. a. B + C gives, gives, Some locks are pens pens.. I is the conversion of this conclusion. Also II and III form a complementary complementary pair. pair. 56. 56. c. B + C gives, gives, Some questions are poets. poets. II is obvious from this. 59. 59. b. The conclusion conclusion drawn drawn from these three statements is All is All flowers are trees. trees. So I is invalid. II can be re-written re-written as, Some trees are flowers. flowers. This is obvious from the derived conclusion.