Proof by contrapositive Prove that if the product $ab$ is irrational, then either $a$ or $b$ (or both) must be irrational.
How do I prove this by contrapositive? What is contrapositive?

If you have to prove an implication $A\Rightarrow B$, contrapositive means you want to prove the equivalent statement $\neg B\Rightarrow\neg A$. The fact that they are equivalent guarantees you that also $A\Rightarrow B$ holds.
In your case, $A=$ 'the product $ab$ is irrational', while $B=$ '$a$ or $b$ must be irrational'. So you just have to negate both $A$ and $B$ and prove the contraposition $\neg B\Rightarrow\neg A$, which is not hard in your case.
By the way, there even is a Wikipedia page with exactly the title of your post here ;)
