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?

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

Hint:

When analyzing logical conclusions based on set relations, consider whether the statements provide enough information to make the conclusions valid.

Answer 1

The Correct Option is C

We are given two statements: - Statement 1: "All purple are green" means that all purple objects are a subset of green objects.
- Statement 2: "All black are green" means that all black objects are also a subset of green objects.
Now, let's examine the conclusions: - Conclusion I: "Some black are purple" suggests that some black objects are also purple. This is not necessarily true based on the given statements, because the black objects are green but there is no direct information implying that any black objects must be purple. Thus, conclusion I is not logically correct.
- Conclusion II: "No black is purple" suggests that none of the black objects are purple. This is a valid conclusion because we know that all purple objects are green, and all black objects are also green. However, the two sets (black and purple) are not required to overlap based on the given statements. Therefore, conclusion II is logically correct.
Since conclusion II is correct, the correct answer is (C), which states that either conclusion I or II is correct.
Final Answer: Either conclusion I or II is correct.