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Incorrect Theorem. Let H be a finite set of n horses. Suppose that, for every subset...

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Advance Math

Incorrect Theorem. Let H be a finite set of n horses. Supposethat, for every subset S ⊂ H with |S| < n, the horses in S areall the same color. Then every horse in H is the same color.

i) Prove the theorem assuming n ≥ 3.

ii) Why aren’t all horses the same color? That is, why doesn’tyour proof work for n = 2?

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