In each of the questions given below, two conclusions are stated followed by five sets of statements. You must assume the conclusions to be true even if they contradict commonly known facts. Determine for which set of statements both conclusions logically follow.

**Conclusions:**

I. Some ball being not box is not a possibility.

II. No box being bottle is a possibility.

**Statements:**

Question

In each of the questions given below, two conclusions are stated followed by five sets of statements. You must assume the conclusions to be true even if they contradict commonly known facts. Determine for which set of statements both conclusions logically follow.

**Conclusions:**

I. Some ball being not box is not a possibility.

II. No box being bottle is a possibility.

**Statements:**

Accepted Answer

**Solution:**

1. We need to verify both conclusions for each set of statements assuming the conclusions are true regardless of common knowledge.

2. **Conclusion I:** "Some ball being not box is not a possibility" means every ball must be a box or at least no ball can be outside the box category.

3. **Conclusion II:** "No box being bottle is a possibility" means it is possible that no box is a bottle.

4. Analyze option (d):
   - "Some water is not bottle" implies some water is outside bottle.
   - "Only ball is colour" means all colours are balls.
   - "All bottle is ball" means every bottle is a ball.
   - "All box is water" means every box is water.

5. From these:
   - Since all box are water and some water is not bottle, some box is not bottle.
   - All bottle is ball, so bottle is a subset of ball.
   - Since some water is not bottle and all box is water, some box is not bottle, so no box being bottle is possible (Conclusion II holds).
   - Also, since all bottle is ball and some water is not bottle, and all box is water, it implies some ball are not box is not possible (Conclusion I holds).

6. Other options fail to satisfy both conclusions simultaneously.

**Answer:** (d)

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