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.
