Exercise 1.7¶
If we take the contrapositive of the statement
\[x^2 \text{ is odd} \Rightarrow x \text{ is odd}\]
then we should end up with
\[x \text{ is not odd} \Rightarrow x^2 \text{ is not odd}.\]
A more sensible way of saying “\(x\) is not odd” is to say “\(x\) is even”, so this statement is equivalent to the statement
\[x \text{ is even} \Rightarrow x^2 \text{ is even}.\]
And we’ve already proved that this is true, so we are done!