GATE EC 2021 Set 1 — Question 6

MCQ+2 / -0.67MediumDeduction & InductionAnalytical AptitudeGeneral Aptitude

General Aptitude → Analytical Aptitude → Deduction & Induction

Last updated 5 September 2026

Question

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?

Correct answer (C) Either conclusion I or II is correct. Solution From the statements, both the set of 'purple' items and the set of 'black' items are subsets of 'green' items. However, no information is provided regarding the relationship between 'purple' and 'black'. They could either overlap (Conclusion I: Some black are purple) or be completely disjoint (Conclusion II: No black is purple). Since these two conclusions are mutually exclusive and exhaustive for the relationship between the two sets, either Conclusion I or Conclusion II must be true. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (C) Either conclusion I or II is correct. Solution From the statements, both the set of 'purple' items and the set of 'black' items are subsets of 'green' items. However, no information is provided regarding the relationship between 'purple' and 'black'. They could either overlap (Conclusion I: Some black are purple) or be completely disjoint (Conclusion II: No black is purple). Since these two conclusions are mutually exclusive and exhaustive for the relationship between the two sets, either Conclusion I or Conclusion II must be true.

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