Prove that if the product ab is irrational, then either a or b (or both) must be irrational.
^^ How do i prove by contrapositive in this? 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 ;)
The statement you want to prove is:
The contrapositive is:
A more natural way to state this (using DeMorgan's Law) is:
This last statement is indeed true. Since the truth of a statement and the truth of its contrapositive always agree, one can conclude the original statement is true, as well.