Given below are three statements and four conclusions drawn based on the statements.
Statement I: Some engineers are writers.
Statement II: No writer is an actor.
Statement III: All actors are engineers.
Conclusion I: Some writers are engineers.
Conclusion II: All engineers are actors.
Conclusion III: No actor is a writer.
Conclusion IV: Some actors are writers.
Which of the following options is correct?
A. Only conclusion I is correct
B. Only conclusions II and III are correct
C. Only conclusions I and III are correct
D. Either conclusion I or conclusion IV is correct
GATE 2022 · General Aptitude · Statements Follow · medium
Answer: Only conclusions I and III are correct (option C).
Evaluate Conclusion I: Statement I says 'Some engineers are writers' -> there exists x such that x is an engineer AND x is a writer. By symmetry, x is also a writer AND an engineer. So 'Some writers are engineers' is TRUE.
Evaluate Conclusion II: Statement III: All actors are engineers (A -> E). Conclusion II claims All engineers are actors (E -> A). This is the CONVERSE of Statement III and does NOT necessarily follow. Conclusion II is FALSE.
Evaluate Conclusion III: Statement II: No writer is an actor. In set terms W and A are disjoint. Disjointness is symmetric: if no writer is an actor, then no actor is a writer. Conclusion III (No actor is a writer) is TRUE.
Evaluate Conclusion IV: Conclusion IV says 'Some actors are writers'. But Statement II says no writer is an actor (W and A are disjoint). This directly contradicts Conclusion IV. Conclusion IV is FALSE.
Select the correct option: Conclusions I and III are correct, II and IV are incorrect. This matches option C.