Three statements are given followed by four conclusions numbered 1, 2, 3, and 4. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically does NOT follow from the statements.

**Statements:**
- All P are G.
- Some G are B.
- All B are C.

**Conclusions:**
1) All P being C is a possibility.
2) Some P are B.
3) Some C are G.
4) Some G are P.

Question

Three statements are given followed by four conclusions numbered 1, 2, 3, and 4. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically does NOT follow from the statements.

**Statements:**
- All P are G.
- Some G are B.
- All B are C.

**Conclusions:**
1) All P being C is a possibility.
2) Some P are B.
3) Some C are G.
4) Some G are P.

Accepted Answer

**Solution:**

1. From the statements:
   - All P are G.
   - Some G are B.
   - All B are C.

2. Analyze each conclusion:

- **Conclusion 1:** All P being C is a possibility.
  - Since all B are C and some G are B, some G are C.
  - All P are G, so it is possible that all P are within C (if P overlaps with the part of G that is C).
  - Hence, this is a possibility and logically follows.

- **Conclusion 2:** Some P are B.
  - All P are G, but only some G are B.
  - There is no definite information that any P is B; the 'some G are B' may or may not include P.
  - Therefore, this conclusion does NOT logically follow.

- **Conclusion 3:** Some C are G.
  - Since some G are B and all B are C, some C are definitely G.
  - This conclusion logically follows.

- **Conclusion 4:** Some G are P.
  - Since all P are G, some G are definitely P.
  - This conclusion logically follows.

**Answer:** Only conclusion 2 does not logically follow from the statements.

Answer

Answer

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