Question

Prove that if n is a positive integer, then n is even if and only if 7n + 4 is even.

Answer 1

Original Statement: if n is a positive integer then n is even if and only if is7n+4 is even. Contrapositive: If n is negative integer then n is odd if and only if 7n+4 is odd. Therefore by definition of odd: n = 2k+1 Substituten: =7(2k+1)+4 =14k+7+4 =14k+11 =2(7k)+11 Therefore, n is odd and7n+4 is odd.