In each of the following questions there are three statements. Which are…
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In each of the following questions there are three statements. Which are followed by three or four conclusions. Choose the conclusions which logically follow from the given statements.
Statements: All the bottles are boxes. All the boxes are bags. Some bags are trays.
Conclusions:
1. Some bottles are trays.
2. Some trays are boxes.
3. All the bottles are bags.
4. Some trays are bags
- A.
Only (3) and (4)
- B.
Only (1) and (2)
- C.
Only (2) and (3)
- D.
Only (1) and (4)
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Correct answer: A
Answer: Only (3) and (4) follow.
Given statements: All bottles are boxes. All boxes are bags. Some bags are trays.
Conclusion 1 — "Some bottles are trays": Does not follow. Reason: All bottles are inside bags, and some bags are trays, but the specific bags that are trays may not contain any bottles. There is no information ensuring overlap between bottles and trays.
Conclusion 2 — "Some trays are boxes": Does not follow. Reason: Boxes are a subset of bags, but the given overlap between trays and bags could lie entirely outside the boxes; nothing guarantees any tray is also a box.
Conclusion 3 — "All the bottles are bags": Follows. Reason: From "All bottles are boxes" and "All boxes are bags" we get by transitivity that all bottles are bags.
Conclusion 4 — "Some trays are bags": Follows. Reason: "Some bags are trays" asserts existence of at least one object that is both a bag and a tray, which equivalently means some trays are bags.
Therefore, only conclusions 3 and 4 follow.