Z, if n2 is odd, then n is odd. 2. We are asked to prove, using the method of contraposition, the
statement: "nZ, if n2 is odd, then n is odd.
The contrapositive of the above statement is: "n
Z, if n is not odd, then n2 is not
odd, or equivalently "nZ,
if n is even, then n2 is even.
Now prove "nZ,
if n is even, then n2 is even by a direct proof.
That is, start by supposing that n is an even integer which means that n = 2k for some
integer k. Then show that n2 must also be even.