contrapositive
example 1
proposition
Let $x, y \in \mathbb{Z}$. If x + y is even, then x and y have the same parity.
Proof
${\neg Q}$: Suppose $x$ and $y$ have opposite parity. Without loss of generality (WLOG), let $x$ be even, so $y$ is odd.
Then there exist integers a and b such that $x = 2a$ and $y = 2b+1$. Then $x+y = 2a + 2b + 1 = 2(a+b) + 1$.
Since, $a+b$ is an integer, $x + y$ is odd. Which is ${\neg P}$
So, because ${\neg Q \Rightarrow \neg P}$ we can say that ${P \Rightarrow Q}$