Question

show that every positive integer is either even or odd​

Answer 1

Step-by-step explanation:

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.

Answer 2

Answer:

The basic concept is that "when a positive integer 'n' is either odd or even then '(n + 1)' is also either even or odd. Case 1:- When 'n' is an odd number. For example, 'n = 2k + 1', where 'k' is an integer, then, (n +1) = (2k+1) + 1.

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