Examine the following statements : 1. All colours are pleasant. 2. Some colours are pleasant. 3. No colour is pleasant. 4. Some colours are not pleasant. Given that statement 4 is true, what can be definitely concluded?
- (a) 1 and 2 are true.
- (b) 3 is true.
- (c) 2 is false.
- (d) 1 is false. ✓ UPSC's answer
Why the answer is (d)
• Statement 4 states 'Some colours are not pleasant,' which is a particular negative proposition (O-type) in categorical logic.
• In the traditional Square of Opposition, the O proposition is contradictory to the A proposition, which is 'All colours are pleasant' (Statement 1).
• Since contradictory propositions always have opposite truth values, if Statement 4 is true, Statement 1 must be false.
• The relationship between Statement 4 (O) and Statement 2 (I, 'Some colours are pleasant') is subcontrary; they can both be true, so Statement 2's truth value cannot be definitively determined.
• The relationship between Statement 4 (O) and Statement 3 (E, 'No colour is pleasant') is subaltern; the truth of the particular does not guarantee the truth of the universal, so Statement 3 cannot be definitively concluded.
• Therefore, the only statement that can be definitely concluded to be false is Statement 1, making option (d) the correct answer.
Why the other options are wrong
- (a) 1 and 2 are true.
- Statement 1 is false because it contradicts Statement 4, and Statement 2's truth value is indeterminate.
- (b) 3 is true.
- Statement 3 is a universal negative that cannot be inferred from the particular negative Statement 4.
- (c) 2 is false.
- Statement 2 is a particular affirmative that can be true simultaneously with Statement 4, so it is not necessarily false.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.