QB_PH_GA_010: Verbal Aptitude

Statements: I. All physicists are mathematicians. II. Some mathematicians are philosophers. Conclusions: 1. Some physicists are philosophers. 2. Some mathematicians are physicists. Which of the conclusion(s) logically follows from the statements?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Set-Theoretic Representation**: - Let $P$ = set of physicists, $M$ = set of mathematicians, $\Phi$ = set of philosophers. - Statement I: $P \subseteq M$. - Statement II: $M \cap \Phi \neq \emptyset$. 2. **Conclusion 1 ($P \cap \Phi \neq \emptyset$)**: - $\Phi$ intersects $M$, but this intersection may lie entirely in $M \setminus P$. - Therefore, $P \cap \Phi$ could be empty. Conclusion 1 does NOT necessarily follow. 3. **Conclusion 2 ($M \cap P \neq \emptyset$)**: - Since $P \subseteq M$ and $P$ is non-empty, $M \cap P = P \neq \emptyset$. - 'Some mathematicians are physicists' is universally valid. Conclusion 2 DOES follow. 4. **Conclusion**: Only conclusion 2 follows. Option (A) is correct.