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GATE 2021 EC – Question 6

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

Given below are two statements and two conclusions.

Statement 1: All purple are green.

Statement 2: All black are green.

Conclusion I: Some black are purple.

Conclusion II: No black is purple.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

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

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Show answer and explanation

Correct answer: (C) Either conclusion I or II is correct.

Explanation

Both statements only tell us that purple and black are subsets of green; they say nothing about how purple and black relate. Conclusion I ("some black are purple") and Conclusion II ("no black is purple") are contradictories, so exactly one of them must hold, but neither is forced alone. Hence "either I or II" is correct.