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Read the given statements, and conclusio...

Read the given statements, and conclusions carefully and select which of the conclusions logically follow(s) from the Statement(s).
Statements:
No Raccoon is Fox
Some Fox are Hyena
Conclusions:
1. Some Hyena are Foxes
2. Some Foxes are Raccoons
3. No Raccoon is Hyena

A

Only conclusion 2 follows

B

All the conclusions follow

C

Only conclusion 3 follows

D

Only conclusion 1 follows

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we will analyze the given statements and conclusions step by step. ### Step 1: Analyze the Statements 1. **Statement 1**: No Raccoon is Fox. - This means that the sets of Raccoons and Foxes do not overlap at all. 2. **Statement 2**: Some Fox are Hyena. - This indicates that there is an overlap between the sets of Foxes and Hyenas, meaning at least some Foxes are also Hyenas. ### Step 2: Draw a Venn Diagram - Draw three circles: - Circle A for Raccoons (R) - Circle B for Foxes (F) - Circle C for Hyenas (H) - According to Statement 1, Circle A (Raccoons) and Circle B (Foxes) do not intersect. - According to Statement 2, Circle B (Foxes) and Circle C (Hyenas) have some intersection. ### Step 3: Analyze the Conclusions 1. **Conclusion 1**: Some Hyena are Foxes. - Since we established that some Foxes are Hyenas, this conclusion logically follows from the statements. **(True)** 2. **Conclusion 2**: Some Foxes are Raccoons. - This contradicts Statement 1, which states that no Raccoon is a Fox. Therefore, this conclusion does not follow. **(False)** 3. **Conclusion 3**: No Raccoon is Hyena. - The statements do not provide any information about the relationship between Raccoons and Hyenas. Therefore, we cannot conclude that no Raccoon is a Hyena. This conclusion cannot be determined to be true or false based on the given statements. **(False)** ### Final Conclusion Based on the analysis: - Only Conclusion 1 logically follows from the statements. ### Summary of the Solution - **Conclusion 1**: True - **Conclusion 2**: False - **Conclusion 3**: False Thus, the answer is that only Conclusion 1 follows.
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