Logical Reasoning

Statements: All pens are books. All books are tables. Conclusions: I. All pens are tables. II. Some tables are pens.

Solution. Pens inside books inside tables, in every legal drawing → I follows. From "all pens are tables", some tables are pens → II follows. Both follow.

Statements: Some cats are dogs. Some dogs are rats. Conclusions: I. Some cats are rats. II. No cat is a rat.

Solution. Cats and rats may overlap, or may not — both drawings are legal, so neither conclusion follows on its own. But the two together cover every case and overlap in none → either I or II follows.

Statements: All fruits are sweet. No sweet thing is bitter. Conclusions: I. No fruit is bitter. II. Some bitter things are fruits.

Solution. Fruits lie inside sweet, which is separate from bitter → I follows in every drawing; II contradicts it → only I follows.

Statements: Some books are pens. All pens are red. Conclusions: I. Some books are red. II. All books are red.

Solution. The books that are pens are red → I follows. II fails in the drawing where other books lie outside red → only I follows.

Statements: All roses are flowers. Some flowers are red. Conclusion: All roses being red is a possibility.

Solution. A legal drawing exists with every rose inside the red region → the possibility holds.

Statement: Only boys can play. Conclusion: All who play are boys.

Solution. "Only A are B" means all B are A → the conclusion follows. Note it does not mean that all boys play.

Statements: All A are B. No B is C. Some C are D. Conclusions: I. No A is C. II. Some D are not B.

Solution. A inside B, and B separate from C → I follows. The C's that are D lie outside B, so some D are not B → II follows. Both follow.

Which set of statements makes "Some pens are papers" definitely true? (a) All pens are books, all books are papers (b) Some pens are books, some books are papers

Solution. (a) — pens inside books inside papers forces the overlap. In (b) the middle term connects nothing.

Statement: Most of the students in the class passed the examination. Conclusion: All the students studied hard.

Solution. "Most" does not give "all", and studying hard is nowhere in the statement → does not follow.

Statement: All the trains from this station run to the east. Conclusion: No train from this station runs to the west.

Solution. Forced by the statement → follows.

Statement: The sale of electric scooters in Delhi rose 40% last year. Conclusion: Electric scooters are becoming popular across India.

Solution. One city does not settle a country → does not follow.

Statement: The company has decided to raise the salaries of its workers from next month. Conclusions: I. The workers were dissatisfied with their salaries. II. The company can afford the rise.

Solution. I is a guess about the reason → does not follow. II is implied by the decision to make it → only II follows.

Statement: "Use our detergent for whiter clothes" — an advertisement. Which is an assumption? (a) People want whiter clothes. (b) The detergent is cheap.

Solution. (a) — the advertisement makes no sense unless whiteness is wanted. Price is not taken for granted anywhere.

Statement: A large number of road accidents on the highway occur at night at one particular curve. Courses: I. The curve should be re-designed and lit. II. The highway should be closed at night.

Solution. I is relevant, practical and proportionate → follows. II is disproportionate → only I follows.

Statement: A sudden outbreak of a water-borne disease has been reported in a locality. Courses: I. The water supply of the locality should be tested at once. II. Residents should be advised to boil drinking water until further notice.

Solution. Both are relevant, practical and immediate → both follow.

Statement: Many students of the school scored poorly in mathematics this year. Courses: I. The mathematics teacher should be dismissed. II. Mathematics should be removed from the syllabus.

Solution. I is punitive before any enquiry; II is absurd → neither follows. (A remedial class would have followed.)

Statement: "Buy our insurance policy and secure your family's future." Assumption: I. People are concerned about their family's future. II. Insurance is the only way to secure it.

Solution. Negate I: nobody cares about their family's future → the appeal collapses → implicit. Negate II: there are other ways → the appeal still works → not implicit. Only I is implicit.

Statement: "Candidates should reach the centre by 9 a.m." — an examination notice. Assumption: I. Candidates can read the notice. II. Candidates will be refused entry after 9 a.m.

Solution. I is necessary for the notice to function → implicit. II is a guess about consequences → not implicit. Only I.

Statement: "The new bridge has reduced travel time between the two towns by an hour." Assumption: Travel time between the towns has fallen.

Solution. That is stated, not assumed → not an implicit assumption.

Question: Should helmets be made compulsory for two-wheeler riders? Argument: Yes — head injuries are the leading cause of death in two-wheeler accidents, and helmets reduce them substantially.

Solution. Relevant and weighty → strong.

Same question. Argument: No — helmets spoil the rider's hairstyle.

Solution. Relevant to the rider's comfort but trivial next to the issue → weak.

Question: Should examinations be held online? Argument: Yes — because that is the modern way and everything should be modern.

Solution. An assertion with nothing behind it, assuming what it should prove → weak.

Question: Should public transport fares be subsidised? Arguments: I. Yes — it puts travel within reach of low-income workers who have no alternative. II. No — subsidies strain the state budget and squeeze spending on health and schools.

Solution. Both are relevant and consequential → both are strong, though they point opposite ways.

Question: Should the school day start an hour later? Arguments: I. Yes — students like sleeping longer. II. No — schools have always started at the same time.

Solution. I is an appeal to preference; II is an appeal to tradition → neither is strong.