Question

Given below are two statements and four conclusions drawn based on the statements.
Statement 1: Some bottles are cups.
Statement 2: All cups are knives.
Conclusion I: Some bottles are knives.
Conclusion II: Some knives are cups.
Conclusion III: All cups are bottles.
Conclusion IV: All knives are cups.
Which one of the following options can be logically inferred?

• A. Only conclusion I and conclusion II are correct
• B. Only conclusion II and conclusion III are correct
• C. Only conclusion II and conclusion IV are correct
• D. Only conclusion III and conclusion IV are correct

Hint:

When analyzing logical deductions, always check if the statements imply the conclusions directly and ensure that the terms in the conclusions are consistent with the premises.

Answer 1

The Correct Option is A

Step 1: Analyzing the statements.
- Statement 1 says "Some bottles are cups," which implies that there is some overlap between bottles and cups.
- Statement 2 says "All cups are knives," which means that all cups are included in the group of knives.
Step 2: Analyzing the conclusions.
- Conclusion I: "Some bottles are knives." This is correct because some bottles are cups (from Statement 1), and all cups are knives (from Statement 2). Therefore, some bottles are also knives.
- Conclusion II: "Some knives are cups." This is also correct because all cups are knives (from Statement 2), so at least the cups are knives.
- Conclusion III: "All cups are bottles." This is incorrect. Statement 1 only says some bottles are cups, not all cups are bottles.
- Conclusion IV: "All knives are cups." This is also incorrect. The statement only tells us that all cups are knives, but it doesn't say all knives are cups.
Step 3: Final Answer.
The correct answer is (A) because only conclusions I and II are logically correct.