Q.10 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, making option (C) the only logically valid conclusion. This syllogism tests deductive reasoning skills common in exams like GATE Life Sciences.
Logical Breakdown
Use Venn diagrams for clarity: Draw a large Researchers circle containing a smaller Professors circle (since all professors are researchers). Overlap some Scientists partially with Professors.
-
This setup guarantees some overlap between Scientists and Researchers via Professors.
-
No full overlaps or exclusions are forced beyond the premises.
Option Analysis
-
(A) All scientists are researchers: Invalid. Only professor-scientists must be researchers; other scientists could exist outside professors.
-
(B) All professors are scientists: Invalid. “Some scientists are professors” doesn’t reverse to include all professors.
-
(C) Some researchers are scientists: Valid. The scientists who are professors are also researchers, creating “some” overlap.
-
(D) No conclusion follows: Invalid, as (C) logically follows from the premises.
Introduction to Syllogism Reasoning
In competitive exams like GATE Life Sciences, syllogism questions test if conclusions logically follow from statements such as “all professors are researchers some scientists are professors logical conclusion.” These assess Venn diagram skills and invalid assumptions, key for analytical ability sections.
Step-by-Step Solution
-
Parse statements: All Professors ⊆ Researchers; some Scientists ∩ Professors ≠ ∅.
-
Test conclusions using distribution: Only particular-affirmative links (some Scientists → Professors → Researchers) hold.
-
Result: (C) follows; others overreach.
| Option | Statement | Valid? | Reason |
|---|---|---|---|
| (A) | All scientists are researchers | No | Undistributed scientists |
| (B) | All professors are scientists | No | Illicit reversal |
| (C) | Some researchers are scientists | Yes | Transitive overlap |
| (D) | No conclusion follows | No | (C) is valid |
GATE Exam Tips
Practice 20+ syllogisms daily, focusing on “some/all” conversions. Use tools like Venn apps for visualization to score 100% in reasoning.
