What does it mean to say that a number x is irrational?

Prove by contradiction statements A and B below, where p and q are real numbers.

A: If pq is irrational, then at least one of p and q is irrational.

B: If p + q is irrational, then at least one of p and q is irrational.

Disprove by means of a counterexample statement C below, where p and q are real numbers.

C: If p and q are irrational, then p + q is irrational.

If the numbers e, pi, pi^2, e^2, e*pi are irrational, prove that at most one of the numbers pi+e, pi-e, pi^2+e^2, pi^2-e^2 is rational.

I'm stuck as where to start with this question.