2. Let n E N and S = {0,1,2,...,2n – 1, 2n}. Suppose that f : S → S is a bijection. Prove that there is some even integer k E S such that f(k) is also even. (State clearly any results you use.)

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2. Let n E N and S
{0,1,2,...,2n – 1,2n}. Suppose that f : S → S is a bijection.
Prove that there is some even integer k E S such that f (k) is also even. (State
clearly any
results
you use.)
Transcribed Image Text:2. Let n E N and S {0,1,2,...,2n – 1,2n}. Suppose that f : S → S is a bijection. Prove that there is some even integer k E S such that f (k) is also even. (State clearly any results you use.)
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