Question

Prove it disprove: if 2n + 4 is even then n is even.

Prove or disprove: if n is even then (n+3)^2 is odd.

Answer 1

The first claim,

"If 2n + 4 is even, then n is even"

is false; as a counterexample, consider n = 1, which is odd, yet 2•1 + 4 = 6 is even.

The second claim,

"If n is even, then (n + 3)² is odd"

is true. This is because

(n + 3)² = n ² + 6n + 9

n ² + 6n is even because n is even. 9 is odd. The sum of an even and odd integer is odd.