Statement:All shoes are legs. Some legs are pairs. Some pairs are hands.…

2023

Statement:

  1. All shoes are legs.

  2. Some legs are pairs.

  3. Some pairs are hands.

Conclusions:

  1. Some hands are shoes.

  2. Some pairs are shoes.

  1. A.

    Only conclusion 1 follows

  2. B.

    Both conclusion 1 and 2 follow

  3. C.

    Neither conclusion 1 nor 2 follows

  4. D.

    Only conclusion 2 follows

Attempted by 116 students.

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Correct answer: C

Solution (textual):

Premises:

  • All shoes are legs.

  • Some legs are pairs.

  • Some pairs are hands.

Examination of conclusions:

  1. 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.

  2. 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.

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