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GATE 2022 XH2 (English) – Question 9

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 2 marks · Multiple choice

Given below are three statements and four conclusions drawn based on the statements.

Statement 1: Some engineers are writers.

Statement 2: No writer is an actor.

Statement 3: 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 one of the following options can be logically inferred?

  1. Only conclusion I is correct
  2. Only conclusion II and conclusion III are correct
  3. Only conclusion I and conclusion III are correct
  4. Either conclusion III or conclusion IV is correct

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Show answer and explanation

Correct answer: (C) Only conclusion I and conclusion III are correct

Explanation

"Some engineers are writers" gives conclusion I. "No writer is an actor" gives conclusion III. Conclusion II does not follow, because the actors are only some of the engineers. Conclusion IV contradicts statement 2, and since III is already true, the "either-or" in D is not a valid inference. So only I and III are correct.