3 CHAPTER 1 The word is also referred to Logic. is an important section of logical reasoning and hence, a working knowledge of its rules is required on the part of the candidate. Hence, it can be expressed as the Science of thought as expressed in language. The questions based on syllogism can be solved by using Venn diagrams and some rules devised with the help of analytical ability. With this unique characteristic, this test becomes an instrument of teaching the candidates to follow the rules and work as per the instructions without an error. Here, only the basic concept and rules, which have a bearing on reasoning faculty could alone help. There are some terminology which are used in syllogism. Proposition It is also referred to as Premises. It is a sentence which asserts that either a part of, or the whole of, one sets of objects-the set identified by the subject term in the sentence expressing that sentence either is included in, or is excluded from, another set-the set identified by the predicate term in that sentence. Types of Proposition Categorical Proposition There is relationship between the subject and the predicate without any condition. Example : I. All beams are logs. II. No rod is stick. Hypothetical Proposition: There is relationship between subject and predicate which is asserted conditionally. Example : I. If it rains he will not come. II. If he comes, I will accompany him. Disjunctive Proposition In a disjunctive proposition the assertion is of alteration. Example : Parts of Proposition It consists of four parts. I. Either he is brave or he is strong. II. Either he is happy or he cannot take revenge. 1. Quantifier: In quantifier the words, all, no and some are used as they express quantity. All and no are universal quantifiers because they refer to every object in a certain set. And quantifier some is a particular quantifier because it refers to at least one existing object in a certain set. 2. Subject: It is the word about which something is said.
3. Predicate: It is the part of proposition which denotes which is affirmed or denied about the subject. 4. Copula: It is the part of proposition which denotes the relation between the subject and predicate. Example : All boys are brilliant Quantifier Subject Copula Predicate Hence, the standard form of proposition is Quantifier + Subject + Copula + Predicate Four-fold classification of categorical proposition: On the basis of quality and quantity of proposition we can classify them in four categories. To draw valid inferences it is necessary to have a clear understanding of the A, E, I, O relationship as given in the table. Symbol Proposition Quantity Quality A All A are B Universal Affirmative E No A is B Universal Negative I Some A are B Particular Affirmative O Some A are not B Particular Negative Rules for Deriving the Conclusions from Two Given Premises 1. Universal affirmative or A-type proposition. Dogs Goats Take an example : All goats are dogs This is A type proposition: We can see it by graphical representation of the above proposition we observe that goats are distributed in dogs. Hence. we can conclude that in A type proposition only subject is distributed. 2. Universal negative or E-type proposition. Boy Girl Take an example : No girl is boy In this type of proposition both subject and predicate are denial of each other. This can also be seen in the diagram representing boy Girl and girl. They have nothing in common. Hence, both subject and predicate are distributed. 3. Particular affirmative or I-type proposition. Mobile Telephone Take an example : Some mobiles are telephones. In this type of proposition subject and predicate have something in common. This implies that in I-type neither subject nor Mobiles Telephones predicate is distributed. We can see it graphically as given in figure.
4. Particular negative or O-type proposition. Boys Students Take an example : Some boys are not students. In O-type propositions some of the category represented by boys subject is not students, which means that a section of boys is denied with the entire category of students. It is, therefore, deduced that in O-type proposition only predicate is distributed. On account of different logical approach required to be applied for drawing each type of inference, a clear understanding of this difference becomes more important. Rules for Mediate Inference First introduced by Aristotle, a syllogism is a deductive argument in which conclusion has to be drawn from two propositions referred to as premises. Now consider an example. Statement: I. Vinay is a boy. II. All boys are honest. Conclusion I. Vinay is honest. First two sentences I and II are called propositions and the sentence I is called conclusion. This conclusion is drawn from above given two propositions. Types of Questions Asked in the Examination There are mainly two types of questions which may be asked under this 1. When premises are in specified form Here premise is in specified form. Here mainly two propositions are given. Propositions may be particular to universal; universal to particular; particular to particular; universal to universal. 2. When premises are in jumbled/mixed form Here at least three or more than three proposition are given. Here pair of two propositions out of them follow as same as in specified form. Type 1 Premises in Specified Forms Case 1: The conclusion does not contain the middle term Middle term is the term common to both the premises and is denoted by M. Hence, for such case, conclusion does not contain any common term belong to both premises. Example 1 Statement: Conclusions I. All men are girls. II. Some girls are students. I. All girls are men. II. Some girls are not students. Solution. Since, both the conclusions I and II contain the middle term girls so neither of them can follow. Venn diagram Representation: All possible cases can be drawn by using Venn diagram. Girls or, Students Girls Men Students men
By using both representation (a) and (b) it is clear all girls cannot be men as well as (a) shows some girls are students, here no man is included but at the same time (b) shows some girls are students have some men are also students as all men are girls. Hence, we cannot deduce conclusion II. So, neither of them can follow. Example 2 Statement: I. All mangoes are chairs. II. Some chairs are tables. Conclusions I. All mangoes are tables. II. Some tables are mangoes. III. No mango is a table. Solution. Here, the term chair is common to both the statement and hence, is the middle term. Statement (I) is A type proposition and in A-type proposition, only subject is distributed, hence, chair being the predicate in the statement (I) is not distributed in the second statement. Thus, none of the conclusions following statement is a valid inference. Venn diagram representation: All possible cases can be drawn as Chairs or, Chairs Mangoes Tables Mangoes Tables (i) All mangoes are table-this inference is definitely false neither (a) nor (b) shows this conclusion. (ii) Some tables are mangoes, this inference is uncertain or doubtful. (iii) No mango is a table, this inference is also uncertain or doubtful. Though it can be concluded from the above discussion that no valid inference can be drawn between mango and table. Case 2: No term can be distributed in the conclusion unless it is distributed in the premises. If case 1 is compiled with by a pair of statement, it is confirmed that valid mediate inferences can be drawn from such pair of statement. But every mediate inference drawn cannot be valid. Therefore, case 2 is applied to check as to the conclusions drawn from a pair of statement in which middle term is distributed, is valid. Example 3 Statement: I. Some boys are students. II. All students are teenagers. Conclusions I. All teenagers are students. II. Some boys are teenagers. Solution. Statement I is an I-type proposition which distributes neither the subject nor the predicate. Statement II is an A type proposition which distributes the subject students. Conclusion I is an A-type proposition which distributes the subject teenagers only. Since. the term teenagers is distributed in conclusion I without being distributed in the premises. So, conclusion I cannot follow. In second conclusion, where it is asked that some boys are teenagers. But from statement I it is clear that some students are not students. These students may not be teenagers. Venn diagram representation: All possible cases can be drawn as follows Boys Students Teenagers.
We have given that all students are teenagers so, its reverse cannot be possible. Hence, conclusion I is false. As we are also given that some boys are students and all students are teenagers. So, some boys which are students must be teenagers. Hence, conclusion II follows. Case 3: If one premises is particular, conclusion is particular. Take an example which explains this case Example 4 Statement: I. Some boys are thieves. II. All thieves are dacoits. Conclusions I. Some boys are dacoits. II. All dacoits are boys. Solution. Since, one premise is particular, the conclusion must be particular. So, conclusion II cannot follow. Venn diagram representation: All possible cases can be drawn as follows Boys Thieves Dacoits Here conclusion I follows but the conclusion II cannot follow. Case 4 If the middle term is distributed twice, the conclusion cannot be universal Take an example which explains such case. Example 5 Statement: Conclusions I. All Lotus are flowers. II. No Lily is a Lotus. I. No Lily is flowers. II. Some Lilies are flowers. Solution. Here, the first premise is an A proposition and so, the middle term Lotus forming the subject is distributed.the second premise is an E proposition and so, the middle term Lotus forming the predicate is distributed. Since, the middle term is distributed twice, so the conclusion cannot be universal. Venn-diagram representation: All possible cases can be drawn as follows Lily Flowers Lotus Lily Flowers Lotus Flowers Lotus It is clear from the given Venn-diagrams either conclusion I or II must be followed. Case 5 If both the premises are affirmative, the conclusions must be affirmative. Take an example which follows such case: Example 6 Statement: I. All gardens are schools. II. All schools are colleges. Conclusions I. All gardens are colleges. II. Some gardens are not colleges.
Solution. Since, both the premises are affirmative, the conclusion must be affirmative, so conclusion II cannot follow. Venn diagram representation: All possible cases can be drawn as follows. Gardens Schools Colleges Now, taking conclusion I, it is clear that all gardens are also colleges. But taking conclusion II, we cannot that derive second conclusion is true. Hence, only the first conclusion must be true. Case 6 No conclusion follows. There are three types of such cases. (a) If both the premises are particular Example 7 Statement: Conclusions I. Some cups are spoons. II. Some spoons are sauccers. I. All cups are sauccers. II. Some sauccers are cups. Solution.Since both the premises are particular, so no definite conclusion follows. Venn diagram representation Sauccers Cups Spoons Cups Sacuccers Spoons It is clear from both given Venn-diagrams that no conclusion is followed. (b) If both the premises are negative Example 8 Statement: I. No flower is mango. II. No mango is cherry. Conclusions I. No flower is cherry. II. Some cherries are mangoes. Solution. Since, both the premises are negative hence, neither conclusion follows. Venn diagram representation: It is clear from both Venn-diagrams that neither conclusion follows. (c) I f the major premise is particular and the minor premise is negative Major premise is the predicate of the conclusion and minor premise is the subject of the conclusion. Example 9 Statement: I. Some pubs are cows. II. No kitten are pubs.
Conclusions I. No pubs are kitten. II. Some cows are kitten. Solution. Here, the first premise containing the middle term Kitten as the subject is the major premise and the second premise containing the middle term Kitten as the predicate is the minor premise. Since, the major premise is particular and the minor premise is negative. So, no conclusion follows. Venn diagram representation: All possible cases are given Puts Cows Kitten Pubs Cows Kitten Pubs Cows Kitten (a) (b) (c) It is clear from the Venn-diagram representation that conclusion I follows. Complementary pair of conclusions In drawing mediate inferences from given statement, students are required to be more attentive in selecting complementary pair of conclusion where neither of the conclusions is definitely true but a combination of both makes a complementary pair. As we have already discussed in case number 1 that in the statement where middle term is not distributed, no valid mediate inference can be drawn but there still exists a possibility that a complementary pair of conclusions follows from the statement. Example 10 Statements I. Some cameras are radios. II. Some statues are cameras. Conclusions I. Some ratios are statues. II. No radio is statue. Solution. Either some radios are statues or No radio is statue follows, as I and E-type proposition form a complementary pair. Venn diagram representation We can draw all possible cases as given below Radios Cameras Radios Cameras Statues Statues Hence, using both diagrammatical representation we can conclude either some radios are statues or no radio is statue. Hence, at least one of the conclusions must be true.
Special Cases Facts Combinations (Conclusion) A + E E + I I + O E + O Conclusion Either I or II follows Either I or II follows Either I or II follows Either I or II follows Example 11 Statements I. All vegetables are green. II. Some greens are fruits. Conclusions I. Some fruits are vegetables. II. No fruit is vegetable. Solution. Here, conclusion I is particular affirmative and conclusion II is universal negative proposition. Hence, either conclusion I or conclusion II follows. Alternatives Green Fruit or Green Vegetables Vegetables Conclusion: If we follow Venn-diagram (a) then we can say no fruit is vegetable. Conclusion II but if we that follow Venn diagram (b) then we can say some fruits are vegetables (conclusion I). Here, either Venn diagram (a) or Venn-diagram (b) is possible. Hence, conclusion I or conclusion II must be followed. Minimal Possibilities We can represent statements by keeping in mind our conclusions It we follow that our two conclusions belong to special case, then either one of them is true. We can represent minimum possibilities as given directly in the statement, we don t need to think about parameters. Example 12 Statements I. Some fruits are vegetables. II. Some vegetables are junk food. III. Some junk foods are snacks. Conclusions I. Some junk foods are vegetables. II. Some junk foods are fruits. Solution. Minimal possibilities Fruit Fruit Vegetables Junk foods Snacks
It is clear from the above diagrams that only conclusion I follows. Type 2 Mixed/jumbled Problems In such type of problem there is a constitution of mixed problems of universal and particular premises. Directions (Q. Nos. 13 to 16) In each of the questions given below there are three statements followed by three conclusions numbered I, II and III, you have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known, facts. Example 13 Statements All halls are tyres. Some tyres are wheels. All wheels are cars. Conclusions I. Some cars are wheels. II. Some cars are tyres. III. Some wheels are halls. (a) None follows (b) Only I follows (c) Only I and II follow (d) Only III follows Solution. (c) Conclusions Cars Tyres Wheels Halls Example 14 I. Some cars are wheels. It can be seen from Venn-diagram. II. Also, some cars are tyres (as shown in Venn-diagram). III. It is not clear from the Venn-diagram. Hence, only I and II follow. Statements Some pictures are frames. Some frames are idols. All idols are curtains. Conclusions I. Some curtains are pictures. II. Some curtains are frames. III. Some idols are frames. (a) Only I and II follow (b) Only II and III follow (c) Only I and III follow (d) All follow Solution. (b)
Conclusions Pictures frames idols Curtains I. Does not follow. II. Follows (clear from the Venn-diagram) III. Follows (clear from the Venn-diagram) Hence, only II and III follow. Example 15 Statements Some ice are rings. No ring is paint. Some rings are gold. Conclusions I. No gold is paint. II. No ice is gold. III. Some rings are paints. IV. All golds are rings. (a) Only I and III follow (b) Only I and II follow (c) Only III and IV follow (d) None follows Solution. (d) Hence, none of the conclusions follows. Ice Rings Gold Paint Example 16 Statements No candle is bell. Some shoes are bells. All tables are shoes. Conclusions I. Some tables are bells. II. No table is bell. III. Some shoes are candles. IV. No shoes are candles. (a) Only I and IV follow (b) Only I and II follow (c) Only III and IV follow (d) None of these Solution. (d) Candles Bells Solution. (d) Here conclusion I is particular affirmative and conclusion II is its universal negative. Hence, either conclusion I or II follows. Also conclusion III is particular affirmative and conclusion IV is its universal negative. Hence, either III or conclusion IV follows. Finally, either conclusion I or II follows and either conclusion III or conclusion IV follows. Table Shoes
Directions (Q. Nos. 1 to 13) In each question given below are two Statements followed by two conclusions numbered I and II. You have to take the two given Statements to be true even if they seem to be at variance from commonly known facts and decide which of the given conclusions logically follows from the the given two Statements, disregarding commonly known facts. Give answer as (a) If only conclusion I follows (b) If only conclusion II follows (c) If neither I nor II follows (d) If both I and II follow 1. Statement: I. All jungles are tigers. II. Some tigers are horses. Conclusions I. Some tigers are jungles. II. All horses are jungles. 2. Statement: I. All birds are tall. II. Some tall are hens. Conclusions I. Some birds are hens. II. Some hens are tall. 3. Statement: I. All artists are smokers. II. Some smokers are drinkers. Conclusions I. All smokers are artists. II. Some drinkers are not smokers. 4. Statement: I. Some hens are cows. II. All cows are horses. Conclusions I. Some horses are hens. II. Some hens are horses. 5. Statement: I. All buses are cars. II. Some cars are roads. Conclusions I. Some cars are buses. II. Some buses are roads. 6. Statement: I. Some pastries are toffees. II. All toffees are chocolates. Conclusions I. Some chocolates are toffees. II. Some toffees are not pastries.. 7. Statement: I. Some players are singers. II. All singers are tall. Conclusions I. Some players are tall. II. All players are tall. EXERCISE 8. Statement: I. All stones are water. II. Some water are clean. Conclusions I. Some water are stones. II. All clear are water. 9. Statement: I. Some phones are watches. II. All watches are guns. Conclusions I. All guns are watches. II. Some guns are phones. 10. Statement: I. All umbrellas are aeroplanes. II. Some aeroplanes are birds. Conclusions I. Some umbrellas are aeroplanes. II. All birds are umbrellas. 11. Statement: I. Some scooters are trucks. II. All trucks are trains. Conclusions I. Some scooters are trains. II. No truck is a scooter. 12. Statement: I. All tigers are ships. II. Some ships are cupboards. Conclusions I. Some ships are tigers. II. Some cupboards are not ships. 13. Statement: I. All books are pencils. II. Some pencils are cycles. Conclusions I. Some cycles are pencils. II. Some cycles are books. Directions (Q. Nos. 14 to 24) In each question below are given two Statements followed by two conclusions numbered I and II. You have to take the given two Statements to be true even if they seem to be at variance from commonly known facts. Read the conclusion and then decide which of the given conclusions logically follows from the given two Statements, disregarding commonly known facts. Give answer as (a) If only conclusion I follows (b) If only conclusion II follows (c) If neither I nor II follows (d) If both I and II follow 14. Statement: I. All men are dogs. II. All dogs are cats. Conclusions I. All men are cats. II. All cats are men.
15. Statement: I. All film stars are playback singers. II. All film directors are film stars. Conclusions I. All film directors are playback singers. II. Some film stars are film directors. 16. Statement: I. All pens are roads. II. All roads are houses. Conclusions I. All houses are pens. II. Some houses are pens. 17. Statement: I. All huts are mansions. II. All mansions are temples. Conclusions I. Some temples are huts. II. Some temples are mansions. 18. Statement: I. All water is divine. II. All temples are divine. Conclusions I. All water is temple. II. All temples are water 19. Statement: I. All cars are cats. II. All fans are cats. Conclusions I. All cars are fans. II. Some fans are cars. 20. Statement: I. All pens are chalks. II. All chairs are chalks. Conclusions I. Some pens are chairs. II. Some chalks are pens. 21. Statement: I. All fans are cups. II. All cups are pillows. Conclusions I. All fans are pillows. II. All pillows are fans. 22. Statement: I. All flowers are stems. II. All stems are roots. Conclusions I. All roots are flowers. II. All stems are flowers. 23. Statement: I. All pencils are bricks. II. All bricks are bottles. Conclusions I. All pencils are bottles. II. All bricks are pencils. 24. Statement: I. All pens are cycles. II. All pigs are cycles. Conclusions I. All cycles are pens. II. All pigs are pens. Directions (Q. Nos. 25 to 40) In each of the question below are given two Statement: s followed by two conclusions numbered I and II. You have to take the two given Statement: s to be true even if they seem to be at variance from commonly known facts and decide which of the given conclusion (s) logically follow (s) from the two given Statement: s, disregarding commonly known facts. Give your answer as (a) If only conclusion or I follows (b) If only conclusion II follows (c) If either I or II follows (d) If both I and II follow 25. Statement: I. Some hats are caps. II. Some caps are mats. Conclusions I. Some caps are hats. II. Some mats are caps. 26. Statement: I. Some fools are intelligent. II. Some intelligent are great. Conclusions I. Some fools are great. II. No great is fool. 27. Statement: I. Some stones are bricks. II. Some bricks are trees. Conclusions I. Some stones are trees. II. Some trees are bricks. 28. Statement: I. Some cities are villages. II. Some towns are villages. Conclusions I. Some cities are towns. II. No town is city. 29. Statement: I. Some visitors are Indians. II. Some visitors are Americans. Conclusions I. Some Indians are visitors. II. All Indians are visitors. 30. Statement: I. Some adults are boys. II. Some boys are old. Conclusions I. Some adults are not old. II. Some boys are not old. 31. Statement: I. Some books are tables. II. Some tables are mirrors. Conclusions I. Some mirrors are books. II. No book is mirror. 32. Statement: I. Some dreams are nights. II. Some nights are days. Conclusions I. All days are either nights or dreams. II. Some days are nights. 33. Statement: I. Some papers are pens. II. Some pencils are pens.
Conclusions I. Some pens are pencils. II. Some pens are papers. 34. Statement: I. Some doctors are fools. II. Some fools are rich. Conclusions I. Some doctors are rich. II. Some rich are doctors. 35. Statement: I. Some clothes are marbles. II. Some marbles are bags. Conclusions I. No cloth is bag. II. Some bags are clothes. 36. Statement: I. Some stones are cups. II. Some cups are black. Conclusions I. No black is cup. II. Some cups are stones. 37. Statement: I. Some pearls are gems. II. Some gems are ornaments. Conclusions I. Some gems are pearls. II. Some pearls are ornaments. 38. Statement: I. Some girls are flowers. II. Some flowers are books. Conclusions I. Some girls are books. II. No book is a girl. 39. Statement: I. Some aeroplanes are living beings. II. Some living beings are ghosts. Conclusions I. Some aeroplanes are ghosts. II. Some aeroplanes are not ghosts. 40. Statement: I. Some cups are plates. II. Some plates are jugs. Conclusions I. Some cups are jugs. II. Some jugs are plates. Directions (Q. Nos. 41 to 50) In each question below are given two statements followed by two conclusions numbered I and II.You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusion and then decide which of the given conclusions logically follows from the two given statements, disregarding known facts. Give answer as (a) If only conclusion I follows (b) If only conclusion II follows (c) If either conclusion I or II follows (d) If neither I nor II follow 41. Statement: I. All roads are poles. II. No pole is a house. Conclusions I. Some roads are houses. II. Some houses are poles. 42. Statement: I. All fish are tortoise. II. No tortoise is a crocodile. Conclusions I. All tortoise is a fish. II. No fish is a crocodile. 43. Statement: I. All windows are doors. II. No door is wall. Conclusions I. No window is wall. II. All door is window. 44. Statement: I. No gentleman is poor. II. All gentlemen are rich. Conclusions I. No poor man is rich. II. No rich man is poor. 45. Statement: I. Some books are pens. II. No pen is pencil. Conclusions I. Some books are pencils. II. No book is pencil. 46. Statement: I. No bat is ball. II. No ball is wicket. Conclusions I. No bat is wicket. II. All wickets are bats. 47. Statement: I. Most teachers are boys. II. Some boys are students. Conclusions I. Some students are boys. II. Some teachers are students. 48. Statement: I. Some books are toys. II. No toy is red. Conclusions I. Some books are red. II. Some toys are books. 49. Statement: I. Some whites are black. II. No black is green. Conclusions I. Some whites are green. II. Some whites are not green. 50. Statement: I. Some pens are pencils. II. No pencil is fruit. Conclusions I. Some pens are fruit. II. Some pencils are pens. Directions (Q. Nos. 51 to 65) In each question below are given two Statements followed by four conclusions numbered I, II, III and IV. You have to take the two given statements to be true even if they seem to be at variance from commonly known
facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given two statements, disregarding commonly known facts. 51. Statement: I. Some doors are mangoes. II. All mangoes are bananas. Conclusions I. All bananas are mangoes. II. All doors are bananas. III. Some doors are bananas. IV. Some mangoes are doors. (a) Only I and II follow (b) None follows (c) All follow (d) Only III and IV follow 52. Statement: I. Some chairs are windows. II. No window is sky. Conclusions I. No window is chair. II. No chair is window. III. Some windows are skies. IV. Some chairs are skies. (a) Either III or IV follows (b) Either II or III follows (c) Either II or IV follows (d) None follows 53. Statement: I. No parrot is crow. II. All crows are bats. Conclusions I. Some bats are parrots. II. All bats are parrots. III. Some bats are crows. IV. Some bats are not crows. (a) Either III or IV follows (b) Only I, II and III follow (c) Only II, III and IV follow (d) Only I and II follow 54. Statement: I. All stars are planets. II. All planets are trees. Conclusions I. All planets are stars. II. All stars are trees. III. All trees are plants. IV. Some trees are stars. (a) Only II and IV follow (b) Only I and II follow (c) None follows (d) All follow 55. Statement: I. Some chairs are shoes. II. Some shoes are sticks. Conclusions I. Some chairs are sticks. II. No chair is stick. III. All sticks are shoes. IV. All shoes are chairs. (a) Either I or II follows (b) Either II or IV follows (c) III follows (d) Only I and II follow 56. Statement: I. All buses are dogs. II. Some dogs are horses. Conclusions I. Some horses are dogs. II. Some dogs are buses. III. Some buses are horses. IV. Some horses are not dogs. (a) Either I or III follows (b) Either II or IV follows (c) Only I and II follow (d) None follow 57. Statement: I. Some tigers are rats. II. Some rats are birds. Conclusions I. Some rats are tigers. II. Some birds are rats. III. Some birds are tigers. IV. Some rats are both birds and tigers. (a) All follow (b) Only I and IV follow (c) Only I and III follow (d) Only II and IV follow 58. Statement: I. Some papers are balls. II. No ball is round. Conclusions I. Some papers are round. II. Some balls are round. III. Some papers are not round. IV. Some balls are papers. (a) Only III follows (b) Only IV follows (c) Either III or IV follows (d) Either I or III and IV follows 59. Statement: I. All maps are roads. II. Some roads are town. Conclusions I. Some towns are maps. II. Some roads are maps. III. No town is a map. IV. All towns are roads. (a) Either I or II follows (b) Either I or III and II follows (c) Only I follows (d) Only IV follows
60. Statement: I. Some trees are pens. II. All pens are pencils. Conclusions I. All pencils are pens. II. All trees are pens. III. Some trees are not pens. IV. All pencils are trees. (a) Only I and II follow (b) Only III and IV follow (c) Only IV follows (d) None of these 61. Statement: I. All papers are bags. II. No bag is green. Conclusions I. No paper is green. II. Some papers are green. III. Some green are papers. IV. Some bags are papers. (a) Either I or II follows (b) Only I and III follow (c) Only I and IV follow (d) None of these 62. Statement: I. All bananas are apples. II. All apples are oranges. Conclusions I. Some oranges are apples. II. All apples are bananas. III. Some bananas are not oranges. IV. Some oranges are bananas. (a) All follow (b) Only I and IV follow (c) Only I and III follow (d) Only I follows 63. Statement: I. Some pens are knives. II. Some knives are horses. Conclusions I. Some knives are pens. II. Some pens are horses. III. Some horses are pens. IV. Some horses are knives. (a) Only II and III follow (b) Only I and IV follow (c) Only IV follows (d) Only I follow 64. Statement: I. No chair is tree. II. All trees are trains. Conclusions I. No chair is train. II. No train is chair. III. Some trains are trees. IV. No train is tree. (a) Only III follows (b) Only III and IV follow (c) Only I and II follow (d) Only II and III follow 65. Statement: I. All buses are roads. II. All roads are rivers. Conclusions I. All buses are rivers. II. Some roads are buses. III. Some rivers are roads. IV. Some rivers are buses. (a) None follows (b) Only I and II follow (c) Only II, III and IV follow (d) All follow Directions (Q. Nos. 66 to 78) Every question below has a few statement, followed by four conclusions numbered I, II, III and IV. You have to consider every given statement as true, even if it goes not conform to the well known facts. Read the conclusions and then decide which of the conclusions can be logically derived. 66. Statement: I. Some toys are pens. II. Some pens are papers. III. Some papers are black. Conclusions I. Some toys are black. II. No pen is black. III. No toy is black. IV. Some pens are black. (a) None of the above (b) Either II or IV (c) Either I or III and either II or IV (d) Either I or IV 67. Statement: I. Some books are copies. II. All copies are green. III. Some green are yellow. Conclusions I. All copies are yellow. II. Some yellow are green. III. Some copies are yellow. IV. All green are copies. (a) Only II follows (b) Either III or IV only (c) Either II or IV only (d) All of these 68. Statement: I. All jugs are glasses. II. All glasses are cups. III. All jugs are pens.
Conclusions I. All pens are jugs. II. Some glasses are pens. III. Some cups are pens. IV. All pens are cups. (a) None follows (b) Only II follows (c) II and III Only (d) III and IV only 69. Statement: I. All Acs are Dcs. II. Some Des are Ecs. III. All Ecs are yys. Conclusions I. Some Acs are Ecs. II. Some yys are Dcs. III. No Acs is Ecs. IV. All Des are Acs. (a) I and III only (b) Only II follows (c) I and II only (d) II and either I or III only 70. Statement: I. Some newspapers are radios. II. Some radios are televisions. III. No television is a magazine. Conclusions I. No newspaper is a magazine. II. No radio is a magazine. III. Some radios are magazines. IV. Some newspapers are televisions. (a) None follows (b) Only III follows (c) Either II or III follows (d) Both I and II follow 71. Statement: I. All crooks are simple. II. Some simple are intelligent. III. All intelligent are fools. Conclusions I. Some fools are crooks. II. No fool is a crooks. III. Some simple are fools. IV. All intelligent are simple. (a) None follows (b) Either I or II follows (c) III and IV follow (d) Either I or II and III follow 72. Statement: I. Some birds are insects. II. All birds are butterflies. III. All insects are snakes. Conclusions I. Some snakes are birds. II. Some butterflies are insects. III. Some snakes are butterflies. IV. Some insects are birds. (a) None follows (b) All follow (c) Only IV follows (d) Either I or III follows 73. Statement: I. All apples are brinjals. II. All brinjals are ladyfingers. III. Some ladyfingers are oranges. Conclusions I. Some oranges are brinjals. II. All brinjals are apples. III. Some apples are oranges. IV. All ladyfingers are apples. (a) None follows (b) Either I or III follows (c) All follow (d) Only I and III follow 74. Statement: I. Some apples are watermelons. II. All watermelons are fresh. III. Some potatoes are fresh. Conclusions I. Some apples are fresh. II. Some potatoes are apples. III. Some watermelons are potatoes. IV. Some watermelons are apples. (a) Only I follows (b) Only I and II follow (c) Only I and IV follow (d) Either II or III and I follow 75. Statement: I. All pens are pencils. II. Some pens are erasers. III. Some erasers are clips. Conclusions I. Some clips are pens. II. No clip is a pen. III. Some erasers are pencils. IV. No eraser is a pencil. (a) Only I and II follow (b) III and either I or II follow (c) Only III follows (d) Either I or II, and either III or IV 76. Statement: I. Some books are papers. II. Some papers are plastic III. No plastic is black. Conclusions I. Some papers are not black. II. All papers are not black. III. Some papers are black. IV. Some books are black. (a) Only I follows (b) Either II or III follows (c) Only I and IV follow (d) Only I, III and IV follow
77. Statement: I. Some doors are windows. II. All windows are black. III. Some black are brown. Conclusions I. Some windows are brown. II. All doors are black. III. Some doors are black. IV. No window is brown. (a) Only III follows (b) Either I or IV and III follow (c) Only II follows (d) Only IV follows ANSWERS 78. Statement: I. All teachers are doctors. II. All doctors are engineers. III. All engineers are typists. Conclusions I. Some typists are teachers. II. All doctors are typists. III. Some engineers are teachers. IV. All doctors are teachers. (a) Only I and II follow (b) Only I and III follow (c) Either II or IV follows (d) None of these 1. (a) 2. (b) 3. (b) 4. (d) 5. (a) 6. (d) 7. (a) 8. (a) 9. (b) 10. (c) 11. (a) 12. (d) 13. (a) 14. (a) 15. (d) 16. (b) 17. (d) 18. (c) 19. (c) 20. (b) 21. (a) 22. (c) 23. (a) 24. (c) 25. (d) 26. (c) 27. (b) 28. (c) 29. (a) 30. (d) 31. (c) 32. (b) 33. (d) 34. (c) 35. (c) 36. (b) 37. (a) 38. (c) 39. (c) 40. (b) 41. (d) 42. (b) 43. (a) 44. (c) 45. (c) 46. (d) 47. (a) 48. (b) 49. (c) 50. (b) 51. (d) 52. (d) 53. (a) 54. (a) 55. (a) 56. (d) 57. (b) 58. (d) 59. (d). 60. (d) 61. (d) 62. (b) 63. (b) 64. (a) 65. (d) 66. (c) 67. (a) 68. (a) 69. (d) 70. (c) 71. (d) 72. (b) 73. (a) 74. (c) 75. (d) 76. (b) 77. (b) 78. (d) EXPLANATIONS 1. Tigers 4. Horses Jungles Horses Hens Cows 2. Hence, only I follows. Tall 5. Hence, both conclusions are true. Cars Birds Hens Buses Roads 3. Hence, from both Venn-diagram conclusion II follows. Smokers Aritist Drinkers 6. Roads Hence, only I follows. Toffees Pastries Chocolates Hence, conclusion I follows. Hence, both I and II are true.
7. Tall 14. Cats Players Singers Dogs Men 8. Hence, some players are tall, only I follows. Water Stones Clean Hence, only I follows. 15. Playback Singers Filmstars 9. Hence, only I follows. Guns Film Directors Phones Watches Hence, both I and II follow. 16. Houses 10. Hence, only II follows. Aeroplanes Roads Pens Umbrellas Birds Hence, only II follows. 11. Hence, none follows. Trains 17. Temples Scooters Trucks Mansions Hence, only I follows. Huts 12. Ships Tigers Cupboards Hence, both I and II follow. 13. Hence, both follow. Pencils 18. Divine Water Divine Books Cycles Temples or, Water Temples Hence, only I follows. Hence, none follows.
19. Cats Cats Cars 24. Cycles Cars Fans Or, Fans Pens Pigs 20. Hence, none follows. Chalks Hence, neither I nor II follows. Pens Charis 25. Mats Mats Hats Caps or, Hats Caps Hence, only II follows. 21. Pillows Cups 26. Hence, both I and II follows. Fools Intelligent Great Fans 27. Hence, eithr I or II follows. Stones Bricks Trees 22. Hence, only I follows. Roots Stems 28. Hence, some trees are bicks (II follows). Cities Villages Towns Flowers Hence, neither I nor II follows. 29. It is a special case. Hence, either conclusion I or conclusion II follows. Hence, either I or II follows. Americans 23. Bottles Bricks Visitors Indian or Visitors Indians Pencils 30. Hence, only I follows. Adults Boys Old Hence, only I follows. Hence, I and II follow.
31. Mirrors 37. Ornaments Books Tables Pearls Gems Hence, either I or II follows. Aliter It is a special case hence, either conclusion I or conclusion II follows. 32. 38. Hence, I follows. Books Girls Flowers 33. Days Dreams Nights Hence, only II follows. Hence, either I or II follows. Aliter It is special case. Hence, either conclusion I or conclusion II follows. 39. Aeroplanes Living beings Pencisl Papers Pens Ghosts 34. Hence, both follow. Rich 40. Hence, either I or II follow. Aliter Its conclusions belong to special case. Jugs 35. Doctors Fools or Doctors Fools Hence, either I or II follows. Aliter It is a special case. Hence, either can conclusion I or conclusion II follows. Cloths Marbles Bags Hence, either I or II follows. Aliter Its conclusions belong to special case. Hence, conclusion I or conclusion II follows. 36. Stones Cups Black Cups Plates Hence, II follows. 41. Poles Roads House Hence, none follows. 42. Tortoise Fish Crocodile Hence, only II follows. 43. Doors Windows Wall Hence, only II follows. Hence, only I follows
44. 52. Gentleman Poor Chairs Windows Sky Rich Hence, either I or II follows. Aliter Its conclusions belong to a special case. Hence, either conclusion I or conclusion II follows. 45. 53. Hence, none follows. Bats Parrot Crow Book Pens Pencil Hence, either I or II is true. Aliter Its conclusions belong to a special case. Hence, either conclusion I or conclusion II follows. 46. Bat Ball Wicket Hence, only III follows. 54. Trees Planets Stars Hence, either I nor II follows. 47. Teachers Boys Students Hence, only II and IV follow. 55. Hence, only I follows. Sticks 48. Books Toys Red Chairs Shoes 49. Hence, only II follows. Whites Hence, either I or II follows. Aliter Its conclusions belong to special case. Hence, either conclusion I or conclusion II follows. Whites Black Green or Green Black 56. 50. Hence, either I or II follows. Aliter Its conclusions belong to a special case. Hence, either conclusions I or conclusion II follows. Dogs Buses Horses 51. Pens Pencils Fruits Hence, only II follows. 57. Hence, only I, II and IV follows. Birds Doors Mangoes Bananas Tigers Rats Hence, both III and IV follow. Hence, only I and IV follows.
58. 63. Paper Ball Round Horses 59. Hence, either I or III and IV follows. Aliter Its conclusions belong to special case. Hence, either conclusion I or conclusion IV follows. Roads Towns 64. Pens Knives Hence, only I and IV follow. Trains Trains Chair Trees or, Chair Trees 60. Maps Hence, either I or III and II follows. Aliter Its conclusions belong to special case. Hence, either conclusion I or conclusion III follows. Pencils 65. Hence, only III follows. Rivers Roads Buses Trees Pens Hence, only III follows. 61. Bags 66. Hence, all follow. Toys Pens Papers Black 62. Papers Green Hence, either I or II and IV follows. Aliter Its conclusions belong to special case. Hence, either conclusion I or conclusion II follows. Organes 67. Here special case can be applied for conclusion I and III also for conclusion II and conclusion IV. Hence, either I or III and II or IV follow. Books Copies Green Yellow Hence, only II follows. 68. Cups Cups Apples Glasses Pens or, Pens Glasses Jugs Jugs Bananas Pens Hence, only I and IV follow. Cups or, Glasses Jugs Hence, none follows.
69. 74. Fresh ACS ECS Apples Watermelon Potatoes 70. DCS YYS Hence, either I or II and III follows. 75. Hence, I and IV follows. Pencils 71. Newspapers Radios Televisions Magazine Hence, either II or III follows. Simple Intelligent Fools Crooks Pens Clips Erasers Hence, either I or II and either III or IV follows. 76. Books Papers Plastic Black 72. Conclusion I and II follow special case. Hence, either I or conclusion II follow. Also from Venndiagram conclusion III follows. Birds Insects 77. Hence, either II or III follows. Black Doors Windows Brown 73. Butterflies Snakes Hence, all follows. Lady fingers Orange 78. Hence, either I or IV and III follows. Typists Engineers Brinjals Doctors Apples Teachers None follows. Hence, only I, II and III follow.