Q.65 All professors are researchers
Some scientists are professors
Which of the given conclusions is logically valid and is inferred from the above arguments:
(A) All scientists are researchers
(B) All professors are scientists
(C) Some researchers are scientists
(D) No conclusion follows
All professors are researchers, and some scientists are professors, logically implies some researchers are scientists as the overlapping professors connect the sets. This validates option (C) through standard syllogistic reasoning. Other options fail due to invalid universal generalizations or reversals.
Syllogism Breakdown
Draw two overlapping circles: Professors entirely within Researchers (universal affirmative). Scientists partially overlap Professors (particular affirmative). The scientists in the professor region are also researchers, confirming some researchers are scientists.
Venn Diagram Logic
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All Professors ⊂ Researchers: No professors outside researchers.
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Some Scientists ∩ Professors ≠ ∅: Shared region exists.
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Thus, Scientists ∩ Researchers ⊃ (Scientists ∩ Professors ∩ Researchers) ≠ ∅, so some researchers are scientists.
Option Analysis
| Option | Conclusion | Valid? | Reason |
|---|---|---|---|
| (A) | All scientists are researchers | No | Only some scientists (those who are professors) must be researchers; others may not be. |
| (B) | All professors are scientists | No | Reverses particular to universal; only some scientists are professors, not vice versa. |
| (C) | Some researchers are scientists | Yes | Follows directly: professors who are scientists are researchers. |
| (D) | No conclusion follows | No | (C) is definitively valid. |
