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?

The statement you want to prove is:

If $ab$ is irrational, then $a$ is irrational or $b$ is irrational.

The contrapositive is:

If not($a$ is irrational or $b$ is irrational), then not($ab$ is irrational).

A more natural way to state this (using DeMorgan's Law) is:

If both $a$ and $b$ are rational, then $ab$ is rational.

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.
