Consider the following statements followed by two conclusions : Statements : Some men are great. Some men are wise. Conclusion I : Men are either great or wise. Conclusion II : Some men are neither great nor wise. Which one of the following is correct ?

(a) Only conclusion I is valid
(b) Only conclusion II is valid
(c) Both the conclusions are valid
(d) Neither of the conclusions is valid ✓ UPSC's answer

Why the answer is (d)

• The statement 'Some men are great' establishes that at least one man is great, but it does not imply that all men are great or that no men are not great.

• Similarly, 'Some men are wise' confirms the existence of wise men but does not exclude the possibility that some men are neither great nor wise.

• Conclusion I claims that every man is either great or wise, which is a universal generalization not supported by the particular premises ('Some').

• Conclusion II claims that some men are neither great nor wise, which is also not necessarily true; it is possible that all men are either great or wise, or that the sets of great and wise men cover the entire group of men.

• Since neither conclusion logically follows from the given premises, the correct answer is that neither conclusion is valid.

Why the other options are wrong

(a) Only conclusion I is valid: Conclusion I is invalid because 'Some men are great' and 'Some men are wise' do not imply that all men are either great or wise.
(b) Only conclusion II is valid: Conclusion II is invalid because the premises do not guarantee the existence of men who are neither great nor wise.
(c) Both the conclusions are valid: Both conclusions are invalid because neither can be logically deduced from the particular statements provided.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.