I'm stuck on a few problems, help on any would be great. Proofs can be either by direct or contraposition.

Prove or disprove that the product of a nonzero rational number and an irrational number is irrational.

Prove that if m and n are integers mn is even, then m is even or n is even

Prove that if n is a positive integer, then n is odd if and only if 5n+6 is odd.