Given the statements:

- Some jackets are shirts.
- Some shirts are trousers.
- No shoes are t-shirts.
- All trousers are shoes.
- All pants are t-shirts.

Which of the following conclusions logically follow?

I. All shirts being t-shirts is a possibility.

II. Some shoes are trousers.

III. Some jackets are t-shirts.

IV. Some shirts being t-shirts is a possibility.

Question

Given the statements:

- Some jackets are shirts.
- Some shirts are trousers.
- No shoes are t-shirts.
- All trousers are shoes.
- All pants are t-shirts.

Which of the following conclusions logically follow?

I. All shirts being t-shirts is a possibility.

II. Some shoes are trousers.

III. Some jackets are t-shirts.

IV. Some shirts being t-shirts is a possibility.

Accepted Answer

**Solution:**

1. From the statements:
   - Some jackets are shirts.
   - Some shirts are trousers.
   - All trousers are shoes.
   - No shoes are t-shirts.
   - All pants are t-shirts.

2. Analyze each conclusion:

- **Conclusion I:** "All shirts being t-shirts is a possibility."
     Since no shoes are t-shirts and all trousers are shoes, shirts (some of which are trousers) cannot be t-shirts fully. Hence, this is not possible.

- **Conclusion II:** "Some shoes are trousers."
     Given all trousers are shoes, it means some shoes are definitely trousers. So, this conclusion follows.

- **Conclusion III:** "Some jackets are t-shirts."
     Jackets are linked to shirts, and shirts are linked to trousers (which are shoes), but no direct link to t-shirts is established. Also, no shoes are t-shirts, so jackets cannot be t-shirts. Hence, this does not follow.

- **Conclusion IV:** "Some shirts being t-shirts is a possibility."
     Since some shirts are not necessarily trousers or shoes, it is possible that some shirts could be t-shirts. So, this conclusion follows.

**Answer:** Only conclusions II and IV logically follow.

Answer

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