Statement:All shoes are legs. Some legs are pairs. Some pairs are hands.…
2023
Statement:
All shoes are legs.
Some legs are pairs.
Some pairs are hands.
Conclusions:
Some hands are shoes.
Some pairs are shoes.
- A.
Only conclusion 1 follows
- B.
Both conclusion 1 and 2 follow
- C.
Neither conclusion 1 nor 2 follows
- D.
Only conclusion 2 follows
Attempted by 116 students.
Show answer & explanation
Correct answer: C
Solution (textual):
Premises:
All shoes are legs.
Some legs are pairs.
Some pairs are hands.
Examination of conclusions:
Conclusion: Some hands are shoes. This does not necessarily follow. There is no premise directly linking hands and shoes. Shoes are contained within legs, while hands are linked to pairs; these regions of legs can be separate, so hands may not overlap shoes.
Conclusion: Some pairs are shoes. This does not necessarily follow. Pairs overlap legs and shoes are a subset of legs, but the part of legs that pairs overlap need not include the part that contains shoes, so pairs and shoes may be disjoint.
Concrete counterexample: Imagine all shoes occupy one region of the legs set. The overlap of pairs with legs occurs in a different region, and that region overlaps hands. Then no hands overlap shoes and no pairs overlap shoes.
Final answer: Neither conclusion follows.