Show that the following statement is true “The integer n is even if and only if n 2 is even”

Question

Philoid · Accepted Answer

Let the statements,

p: Integer n is even

q: If n² is even

Let p be true.

Then

Let n = 2k

Squaring both the sides, we get,

n² = 4k²

n² = 2.2k²

Therefore, n² is an even number.

So, q is true when p is true.

Hence, the statement is true.