Consider two Statements and four Conclusions given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all Conclusions and then decide which of the given Conclusion(s) logically follows/follow from the Statements, disregarding the commonly known facts. Statement-1 : Some greens are blues. Statement-2 : Some blues are blacks. Conclusion-1 : Some greens are blacks. Conclusion-2 : No green is black. Conclusion-3 : All greens are blacks. Conclusion-4 : All blacks are greens. Which one of the following is correct ?
- (a) Conclusion-1 and Conclusion-2 only
- (b) Conclusion-2 and Conclusion-3 only
- (c) Conclusion-3 and Conclusion-4 only
- (d) Neither Conclusion 1 nor 2 nor 3 nor 4 ✓ UPSC's answer
Why the answer is (d)
• Statement 1 states that some Greens are Blues, establishing an overlap between the Green and Blue sets.
• Statement 2 states that some Blues are Blacks, establishing an overlap between the Blue and Black sets.
• In syllogistic logic, when two premises are both particular (starting with 'Some'), no definite conclusion can be drawn about the relationship between the first and last terms (Green and Black).
• The 'Blues' in Statement 1 and the 'Blues' in Statement 2 may or may not be the same specific individuals; therefore, there is no guaranteed connection between Greens and Blacks.
• Since no definite relationship (intersection, exclusion, or inclusion) can be established between Greens and Blacks, none of the four conclusions logically follow.
• Thus, the correct option is (d), as neither Conclusion 1, 2, 3, nor 4 is valid.
Why the other options are wrong
- (a) Conclusion-1 and Conclusion-2 only
- Conclusion 1 does not follow because the 'Blues' linking Greens and Blacks are not necessarily the same, and Conclusion 2 is not definitively true as an overlap is possible.
- (b) Conclusion-2 and Conclusion-3 only
- Conclusion 2 is not necessarily true because Greens and Blacks might overlap, and Conclusion 3 is false because there is no evidence that all Greens are Blacks.
- (c) Conclusion-3 and Conclusion-4 only
- Conclusion 3 is false because there is no evidence that all Greens are Blacks, and Conclusion 4 is false because there is no evidence that all Blacks are Greens.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.