Inference is a process of passing from one or more prepositions to another which is justified by them. In deductive inference, the conclusion cannot be more general than the premises. In mediate deductive inference or syllogism, the inference is derived from two premises which have a common term known as the middle term. A syllogism consists of three prepositions (two given prepositions and preposition inferred from the given prepositions). The inferred preposition is called the conclusion. Two given prepositions are called the premises. Each preposition consists of two terms. Therefore, a syllogism consists of six terms. The three terms each of which occurs twice, have different names given to them. The predicate of the conclusion is called the Major Term. The subject of the conclusion is called the B. The term which occurs in both the premises but does not occur in conclusion, is called the Middle Term. The premise in which the major term occurs is called the Major Premise and the premise in which the minor term occurs, is called the Minor Premise. For example : All boys are desks All windows are boys Therefore, All windows are desks. Here the term desks is a Major Term, Windows is a Minor Term being the Predicate and the Subject of the conclusion respectively. The term boys which occurs in both the premises but is absent from the conclusion, is the Middle Term. The first premise All boys are desks is the Major premise the second premise All windows are boys is the Minor premise. When a syllogism is given in its strict logical form, the major premise comes first, then comes the minor premise and in the end comes the conclusion. A term is said to be distributed in a preposition when it is taken in its entire denotation and it is undistributed when only a part of it is considered. Let S and P denote the subject and predicate respectively. Consider A : All S is P E : No S is P Here, subject term is distributed in both the statements A & E while predicate term is distributed in E only and not in A. Consider I : Some S is P O : Some S is not P Here, subject term is undistributed in both the statements I & O while predicate term is distributed in O only and no in I. Consider A : All S is P I : Some S is P Here, predicate term is undistributed in both the statements A & I while subject term is distributed in O only and not in I. Consider E : No S is P O : Some S is not P Here, predicate term is distributed in both the statement E & O. While subject term is distributed in E only and not in O. General Rules of Categorical Syllogism 1. Every syllogism must contain three and only three terms. 2. The middle term must be distributed at least once in the premises. Example : All boys are desks All windows are desks All windows are boys violates rule 2. The middle term desk is not distributed in the premises even once. 3. No term can be distributed in the conclusion unless it is distributed in the premise. Example : All boys are desks No windows are boys No windows are desks violates rule 3. The term desks is distributed in the conclusion without being distributed in the premises. 4. From two negative premises, no conclusion can be drawn. 5. If one premise is negative, the conclusion is negative and vice-versa. 6. If both the premises are affirmative, the conclusion is affirmative and vice-versa. Figures of Syllogism First Figure : In the first figure, middle term is the subject in the major premise and the predicate in the minor premise. The valid conclusions which can be drawn from two given statements are indicated below : (1) AA A e.g. : All boys are desks All windows are boys All windows are desks (2) AE X e.g. : All boys are desks No windows is a boy Here, no conclusion follows because any conclusion would distribute P which is not distributed in premise A. (3) AI I e.g. : All boys are desks Some windows are boys Some windows are desks (4) AO X e.g. : All boys are desks Some windows are not boys Here, no conclusion follows because any conclusion would distribute P which is not distributed in premise A. (5) EA E e.g. : No desks are windows All boys are desks No boys are windows (6) EI O e.g. : No desks are windows Some boys are desks Some boys are not windows (7) IA X e.g. : Some boys are desks All windows are boys No conclusion follows because middle term is not distributed. (8) OA I e.g. : Some boys are not desks All windows are boys No conclusion follows because middle term is not distributed. Second Figure : In the second figure, the middle term is the predicate in both premises. (1) AA X e.g. : All boys are desks All windows are desks No conclusion can be drawn because middle term is not distributed in both the premises. (2) AE E e.g. : All boys are desks No windows are desks No windows are boys (3) AI X e.g. : All boys are desks Some windows are desks No conclusion follows because middle term is not distributed in both the premises. (4) AO O e.g. : All boys are desks Some windows are not desks Some windows are not boys (5) EA E e.g. : No boys are desks All windows are desks No windows are boys (6) EI O e.g. : No boys are desks Some windows are desks Some windows are not boys (7) IA X e.g. : Some boys are not desks All windows are desks Third Figure : In the third figure, the middle term is the subject in both the premises. (1) AA I e.g. : All boys are desks All boys are windows Some windows are desks (2) AE X e.g. : All boys are desks No boy is window (3) AI I e.g. : All boys are desks Some boys are windows Some windows are desks (4) AO X e.g. : All boys are desks Some boys are not windows (5) EA O e.g. : No boy is desk All boys are windows Some windows are not desks (6) EI O e.g. : No boy is desk Some boys are windows Some windows are not desks (7) IA I e.g. : Some boys are desks All boys are windows Some windows are desks (8) OA O e.g. : Some boys are not desks All boys are windows Some windows are not desks Fourth figure : In the fourth figure, the middle term is the predicate in the major premise and the subject in the minor premise. (1) AA I e.g. : All boys are desks All desks are windows Some windows are boys (2) AE E e.g. : All boys are desks No desks are windows No windows are boys (3) AI X e.g. : All boys are desks Some desks are windows (4) AO X e.g. : All boys are desks Some desks are not windows (5) EA O e.g. : No boys are desks All desks are windows Some windows are not boys (6) EI O e.g. : No boy is desk Some desks are windows Some windows are not boys (7) IA I e.g. : Some boys are desks All desks are windows Some windows are boys (8) OA X e.g. : Some boys are not desks All desks are windows LOGICAL REASONING - EVALUATION OF FACTS, CONCLUSIONS AND ARGUMENTS Directions : In the following questions there are two statements followed by two conclusions (a) and (b). You have to take the two given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts. If only conclusion (a) follows, then mark A; if only (b) follows, then mark B; if both (a) and (b) follow, then mark C; if either (a) or (b) follows, then mark D and if neither (a) nor (b) follows, then mark E. 1. Statements : (1) (2) All lamps are poles Some poles are woods Conclusions : (a) (b) Some lamps are woods Some woods are poles 2. Statements : (1) (2) Most tanks are guns Some guns are stones Conclusions : (a) (b) Some stones are guns Some tanks are stones 3. Statements : (1) (2) All windows are boys All boys are desks Conclusions : (a) (b) All windows are desks Some desks are not windows 4. Statements : (1) (2) All cards are cups No cup is glass Conclusions : (a) (b) All cups are cards No card is glass 5. Statements : (1) (2) All chairs are houses Some shoes are houses Conclusions : (a) (b) Some chairs are shoes Some shoes are chairs 6. Statements : (1) (2) Sohan is a good sportsman Sportsmen are generally healthy Conclusions : (a) (b) All healthy persons are sportsmen Sohan is healthy 7. Statements : (1) (2) Some men are educated Educated persons prefer small families Conclusions : (a) (b) All small families are educated Some men prefer small families 8. Statements : (1) (2) All men are chairs All chairs are tables Conclusions : (a) (b) All men are tables Some chairs are men 9. Statements : (1) (2) All boys are rivers Some rivers are girls Conclusions : (a) (b) Some girls are boys Some boys are girls 10. Statements : (1) (2) All birds are parrots Shyam is a parrot Conclusions : (a) (b) Shyam is a bird All parrots are birds 11. Statements : (1) (2) Some bags are cigarettes Some non-bags are tables Conclusions : (a) (b) Some bags are tables All bags are not cigarettes 12. Statements : (1) (2) All writers are men No man is absent Conclusions : (a) (b) There are no women writers All writers are present 13. Statements : (1) (2) Some trains are stations All stations are crowded Conclusions : (a) (b) All trains are crowded All stations are trains 14. Statements : (1) (2) Meena is a book Some books are benches Conclusions : (a) (b) Meena is a tree All books are trees 15. Statements : (1) (2) All books are bananas All bananas are pens Conclusions : (a) (b) All bananas are books All books are pens 16. Statements : (1) (2) Some dramatists are poets All elephants are poets Conclusions : (a) (b) Some dramatists are elephants All poets are elephants 17. Statements : (1) (2) All students are girls No girl is dull Conclusions : (a) (b) There are no boys in the class No student is dull 18. Statements : (1) (2) All cats are books All books are singers Conclusions : (a) (b) All cats are singers All books are cats 19. Statements : (1) (2) Some cats are kittens All goats are kittens Conclusions : (a) (b) Some cats are goats Some goats are cats 20. Statements : (1) (2) All names are houses No houses are foxes Conclusions : (a) (b) All foxes are names No houses are names 21. Statements : (1) (2) All pens are dogs Some pens are lights Conclusions : (a) (b) Some dogs are lights Some lights are not dogs 22. Statements : (1) (2) All plants are engines Some engines are drums Conclusions : (a) (b) Some plants are drums Some drums are plants 23. Statements : (1) (2) All eyes are leaves All leaves are wolves Conclusions : (a) (b) Some wolves are leaves Some wolves are eyes 24. Statements : (1) (2) Some boys are blockhead Gampu is a boy Conclusions : (a) (b) Gampu is a blockhead Gampu is not a blockhead 25. Statements : (1) (2) Some girls are swimmers Charu is a girl Conclusions : (a) (b) Charu is a swimmer Some girls are not swimmers 26. Statements : (1) (2) All hills are mice All mice are men Conclusions : (a) (b) All hills are men All men are hills 27. Statements : (1) (2) Some authors are painters All painters are honest Conclusions : (a) (b) All honest persons are painters Some authors are honest 28. Statements : (1) (2) All tables are horses All horses are rivers Conclusions : (a) (b) All tables are rivers Some rivers are tables 29. Statements : (1) (2) All poets are authors All singers are authors Conclusions : (a) (b) All singers are poets Some authors are not singers 30. Statements : (1) (2) All cats are dogs Some dogs are black Conclusions : (a) (b) Some cats are black Black dogs are not cats 31. Statements : (1) (2) All floors are roofs Some floors are walls Conclusions : (a) (b) Some roofs are walls Some roofs are floors 32. Statements : (1) (2) Some plants are trees Jasmine is a plant Conclusions : (a) (b) Jasmine is a tree Some trees are plants 33. Statements : (1) (2) All stamps are letters All letters are postcards Conclusions : (a) (b) All stamps are postcards Some letters are stamps 34. Statements : (1) (2) All cups are plates Some glasses are plates Conclusions : (a) (b) Some glasses are cups Some cups are glasses 35. Statements : (1) (2) No doors are windows Some locks are not windows Conclusions : (a) (b) No window is a door Some locks are not doors 36. Statements : (1) (2) Some animals are lions Some lions are mammals Conclusions : (a) (b) All animals are mammals Some animals are mammals 37. Statements : (1) (2) All horses are donkeys All donkeys are dogs Conclusions : (a) (b) All dogs are horses All dogs are donkeys 38. Statements : (1) (2) No mugs are spoons All mugs are forks Conclusions : (a) (b) No forks are spoons Some forks are not spoons 39. Statements : (1) (2) All cars are buses All cycles are buses Conclusions : (a) (b) All cars are cycles All cycles are cars 40. Statements : (1) (2) No books are albums All pictures are books Conclusions : (a) (b) All books are pictures No pictures are albums 41. Statements : (1) (2) If he buys a table, he will not buy chairs He did not buy a table Conclusions : (a) (b) He bought chairs He did not buy chairs 42. Statements : (1) (2) Some men are scholars This writer is a man Conclusions : (a) (b) This writer is a scholar This writer is not a scholar 43. Statements : (1) (2) No teachers are educated people Some poets are educated people Conclusions : (a) (b) Some poets are not teachers Some poets are not educated people 44. Statements : (1) (2) All actors are tall No handsome people are actors Conclusions : (a) (b) Some actors are not handsome people No handsome people are tall 45. Statements : (1) (2) All women are educated No labourers are educated Conclusions : (a) (b) No women are labourers No labourers are women 46. Statements : (1) (2) All ponds are rivers All lakes are rivers Conclusions : (a) (b) Some ponds are rivers Some lakes are ponds 47. Statements : (1) (2) All houses are homes Some homes are dwellings Conclusions : (a) (b) Some houses are dwellings Some dwellings are houses 48. Statements : (1) (2) All fans are coolers Some machines are coolers Conclusions : (a) (b) Some machines are fans Some coolers are machines 49. Statements : (1) (2) Some editors are journalists Some writers are not editors Conclusions : (a) (b) Some writers are not journalists Some editors are not journalists 50. Statements : (1) (2) All teachers are scientists All workers are not scientists Conclusions : (a) (b) All workers are not teachers All scientists are teachers 51. Statements : (1) (2) Some crows are not animals All crows are birds Conclusions : (a) (b) Some birds are not animals Some crows are animals 52. Statements : (1) (2) All streets are roads Some footpaths are streets Conclusions : (a) (b) Some footpaths are roads Some streets are footpaths 53. Statements : (1) (2) No teachers are educated people Some poets are educated people Conclusions : (a) (b) Some poets are not teachers Some poets are not educated people 54. Statements : (1) (2) Some colleges are not universities Some colleges are institutions Conclusions : (a) (b) No institutions are universities Some institutions are not universities 55. Statements : (1) (2) No courier is a postman Some postmen are government servants Conclusions : (a) (b) No postman is a courier Some government servants are not couriers 56. Statements : (1) (2) Some crows are cows Some cows are cats Conclusions : (a) (b) Some crows are cats All crow are cats Directions : 57 - 71. In each question below is given a statement followed by two conclusions numbered I and II. You have to assume everything in the statement to be true, then decide which of the two given conclusions logically follows beyond a reasonable doubt from the information given in the statement. Give answer (A) if only conclusion I follows : give answer (B) if only conclusion II follows; give answer (C) if either I or II follows; give answer (D) if neither I nor II follows and give answer (E) if both I and II follow. 57. Statement : The present approach of International Labour Organisation (ILO), the Minister said, was primarily directed to keep in view the interests of the workers in organized sector only which was not helpful to developing countries where a large number of workers were engaged in the unorganized sector. Conclusions : I. ILO should include interests of workers in unorganized sector in their approach to make it useful for developing countries. II. Developing countries are helpless as regards their workers in unorganized sectors. 58. Statement : Water Supply in wards A to D of the city will be affected by about 25 per cent on Friday because repairing work of the main lines was to be carried out. Conclusions : I. The residents in these wards should economize on water on Friday. II. The residents in these wards should store water on the previous day. 59. Statement : Throughout the Third World women are generally more involved that men in food production, storage and marketing - FAO report. Conclusions : I. Women more than men in the Third World should be trained in new methods for farming if agricultural production is to be increased there. II. Women always work very sincerely. 60. Statement : Water supply in wards A to D of the city will be affected by about 25 per cent on Friday because repairing work of the main lines was to be carried out. Conclusions : I. Such repairs should not inconvenience the residents. II. Such announcements are useful to the residents. 61. Statement : Education is in the concurrent list and therefore, States are unable to reform the education quickly without the consent of the Central Government - an opinion. Conclusions : I. State and Central Governments are not keen to reform education. II. Education should be an exclusively State subject if quick reform is required. 62. Statement : After this amendment to the constitution, no child below the age of 14 years will be employed to work in any factory or mine or engaged in any other hazardous employment. Conclusions : I. Before this amendment, children below 14 years were employed to work in factory or mine. II. The employers must now abide by this amendment to the constitution. 63. Statement : The dissimilarities between the problems of rural and urban development stand out clearly when we compare the attitude of Government towards these two fields. Conclusions : I. Government has more favourable attitude towards rural development than urban development. II. Government has more favourable attitude towards urban development than rural development. 64. Statement : A neurotic is a non-stupid person who behaves stupidly. Conclusions : I. Neuroticism and stupidity go hand in hand. II. Normal persons behave intelligently. 65. Statement : Castes on its social side are a product of human organizations and not a mystery of divine appointment. Conclusions : I. Castes are man-made. II. Divinity has created many mysteries in the world. 66. Statement : Constitutional morality is not a natural sentiment. Conclusions : I. Sentiments are innate. II. Constitutional morality is to be cultivated. 67. Statement : It does not matter what type of food you eat. What matters is whether you can digest it. Conclusions : I. Any type of food is equally good as long as it can be digested. II. The type of food one eats is immaterial. 68. Statement : If blue is heavy, yellow is light. If red is light, green is medium. But blue is heavy or red is light. Conclusions : I. Yellow and red are light II. Green is medium. 69. Statement : He questioned the utility of the present procedure and suggested its replacement by another one designed for speedy disposal. Conclusions : I. Procedure should be abolished II. Procedure should be made for speedy disposal. 70. Statement : Now you do not need any import license to own an electronic typewriter. Conclusions : I. Electronic typewriters are now made indigenously. II. Electronic typewriters are now freely permitted for import. 71. Statement : It does not matter what a tonic contains. What matters is what your body gets out of it. Conclusions : I. Any tonic is equally good if the body can absorb it. II. Compositions of a tonic is of no consequence. Directions : Questions 72-74 : In each of the following questions two statement (1) and (2) are given. You have to take these two statements to be true even if they seem to be at variance from commonly known facts and then decide which of the five alternatives (A), (B), (C), (D), and (E), logically follows from the given statements disregarding commonly known facts. 72. Statements : (1) All girls are mothers. (2) Some mothers are children. (A) All girls are children (B) Some girls are children (C) All mothers are girls (D) Some children are girls (E) None of the above 73. Statements : (1) Some roots are fruits (2) All roots are trees. (A) All roots which are not fruits, are trees (B) Some fruits are trees (C) There may be roots which are neither fruits nor trees (D) All the roots are either fruits or trees (E) None of the above. 74. Statements : (1) All children are chairs (2) All cats are children (A) All cats are chairs. (B) Some children are cats. (C) No cat is chair (D) Some chairs are cats (E) None of the above. Directions : Questions 75-79 : In each of the following questions there are two statements (1) and (2) followed by a conclusion. If only statement (1) supports the conclusion, then mark A; if only statement (2) supports the conclusion, then mark B; if both the statements support the conclusion, then mark C; if either of the two statements supports the conclusion, then mark D and if none of the two statements supports the conclusion, then mark E. 75. Statements : (1) All rocks are mountains (2) All rocks are trees Conclusion : Some mountains are trees 76. Statements : (1) (2) Deficit financing is responsible for rise in prices Deficit financing is essential for development Conclusion : The rise in prices is the key of development. 77. Statements : (1) (2) Some vegetables are fruits Fruits are good for health Conclusion : Some vegetables are good for health 78. Statements : (1) (2) All goods are economic All goods are normal Conclusion : No goods is uneconomic 79. Statements : (1) (2) The growth rate of population is very high in India Excessive increase in population is a hindrance to economic development Conclusion : The population of India stands in the way of the process of economic development. ANSWERS 1.E 2.E 3.A 4.B 5.E 6.E 7.B 8.C 9.E 10.E 11.E 12.C 13.E 14.E 15.B 16.E 17.C 18.A 19.E 20.E 21.A 22.A 23.B 24.D 25.C 26.A 27.B 28.C 29.E 30.E 31.C 32.E 33.C 34.E 35.A 36.C 37.E 38.B 39.E 40.B 41.D 42.D 43.A 44.E 45.C 46.A 47.E 48.E 49.E 50.A 51.A 52.C 53.A 54.E 55.C 56.E 57.A 58.E 59.A 60.B 61.D 62.B 63.C 64.A 65.A 66.E 67.A 68.D 69.B 70.E 71.E 72.E 73.C 74.A 75.E 76.E 77.C 78.A 79.C
Posted on: Sat, 30 Nov 2013 16:52:12 +0000
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