NIMCET 2025 — Reasoning PYQ

1. Analysis of Statements:

• Statement 1: "Some men are great" means $M\cap G\ne \varnothing$. There is at least one man who is great.

• Statement 2: "Some men are wise" means $M\cap W\ne \varnothing$. There is at least one man who is wise.

2. Evaluating Conclusion 1:

"Men are either great or wise."

This is a universal claim implying that the entire set of Men ($M$) must fall into either category $G$ or $W$. However, the statements only tell us about some men. We have no information about the "rest" of the men. They could be neither. Therefore, this does not follow.

3. Evaluating Conclusion 2:

"Some men are neither great nor wise."

While this might seem "common sense," in formal logic, we only go by what is explicitly stated. The statements say "Some men are great." It is possible that all men are great, as "some" is a subset that doesn't strictly exclude "all." Since we cannot prove for certain that there are men outside these categories based only on the premises, this conclusion is a possibility but not a definite certainty.

Conclusion:

Both conclusions fail the test of logical necessity.

Correct Option: (D)