UPSC Prelims 2010 Q131: Science & Technology – Logical Reasoning & Puzzles
- (a) 1 and 2 are true
- (b) 1 is false
- (c) 2 is false
- (d) 3 is true
Answer: (b) 1 is false
Explanation
A categorical-logic puzzle: what follows from "Some colours are not pleasant"?
Given that statement 4 ('Some colours are not pleasant') is true, we apply standard rules of categorical logic.
| Statement | Relationship to statement 4 |
|---|---|
| 1. All colours are pleasant | This is the direct contradictory of statement 4; if 'some are not pleasant' is true, 'all are pleasant' must be false |
| 2. Some colours are pleasant | Not determined — this could be true or false independently; statement 4 alone doesn't fix its truth value |
| 3. No colour is pleasant | Not determined — also independent; 'some are not pleasant' doesn't force 'none are pleasant' to be true |
Why statement 1 is definitely false:
| Point | Detail |
|---|---|
| Logical relationship | 'All A are B' and 'Some A are not B' are contradictories — exactly one must be true, the other false |
| Given | Statement 4 ('some are not pleasant') is true |
| Therefore | Statement 1 ('all are pleasant') is necessarily false |
Answer: (b) 1 is false.
Why each option is right or wrong
- (a) Incorrect. Statements 1 and 2 being both true is impossible, since statement 1 is actually false given statement 4.
- (b) CORRECT. Since 'Some colours are not pleasant' (statement 4) is true, its direct contradictory, 'All colours are pleasant' (statement 1), must be false.
- (c) Incorrect. Statement 2's truth value is not determined by statement 4 alone; it cannot be definitively declared false.
- (d) Incorrect. Statement 3's truth value is also not determined by statement 4 alone.
Key point
Given 'Some colours are not pleasant' (statement 4) is true, its logical CONTRADICTORY, 'All colours are pleasant' (statement 1), must be false — statements 2 and 3's truth values remain undetermined.
Remember
Given 'Some colours are not pleasant' is true, 'All colours are pleasant' must be false — a direct contradictory relationship in categorical logic.
Common mistakes
- Not recognising the contradictory relationship between 'All A are B' and 'Some A are not B' in categorical logic.
- Assuming statement 4's truth also determines the truth of statements 2 or 3, when it doesn't.
- Confusing contrary relationships (where both can be false) with contradictory ones (where exactly one must be false).
Exam tip
'All A are B' and 'Some A are not B' are CONTRADICTORIES — if one is true, the other is definitely false. The other two statement types aren't automatically determined.
Sources
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Syllogism)
- Arun Sharma — How to Prepare for Logical Reasoning for the CAT (propositions and syllogisms)