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? A. Only conclusion I is correct B. Only conclusion II is correct C. Either conclusion I or conclusion II is correct D. Both conclusion I and conclusion II are correct

GATE 2021 · General Aptitude · Statements Follow · medium

Answer: C. Either conclusion I or conclusion II is correct

1. Map what the statements establish: Statement 1: Purple subset Green. Statement 2: Black subset Green. Both sets lie inside Green but no direct connection between Purple and Black is stated.
2. Test Conclusion I: Some black are purple: From the given statements we cannot confirm that black and purple overlap. It is possible that all black things are non-purple (just green). Conclusion I does NOT necessarily follow.
3. Test Conclusion II: No black is purple: From the given statements we cannot confirm that black and purple are disjoint. It is possible that some black things are also purple (both being green is compatible with overlap). Conclusion II does NOT necessarily follow.
4. Apply the complementary pair rule: Conclusion I ('Some black are purple') and Conclusion II ('No black is purple') are logical contradictories. In any possible scenario, exactly one must be true. Since neither is individually proved from the statements, the answer is: Either Conclusion I or Conclusion II is correct.