InterviewSolution
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InterviewSolution
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Show that every positive integer is either even or odd? |
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Answer» Let us assume that there exist a smallest positive integer that is neither odd nor even, say n. Since n is least positive integer which is neither even nor odd, n – 1 must be either odd or even. Case 1: If n – 1 is even, n – 1 = 2k for some k. But this implies n = 2k + 1 this implies n is odd. Case 2: If n – 1 is odd, n – 1 = 2k + 1 for some k. But this implies n = 2k + 2 (k+1) this implies n is even. In both ways we have a contradiction. Thus, every positive integer is either even or odd. |
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