Question

Show that the following statement is true
“The integer n is even if and only if n2 is even”
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Answer 1

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Let the statements,

p: Integer n is even

q: If n^2 is even

Let p be true.

Then

Let n = 2k

Squaring both the sides, we get,

n^2 = 4k^2

n^2 = 2.2k^2

Therefore, n^2 is an even number.

So, q is true when p is true.

Hence, the statement is true.

Hope it helps you..♡

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Answer 2

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