Let  and  be real numbers. If  is irrational, then  is irrational or  is irrational Let  and  be real numbers. If  is irrational, then  is irrational or  is irrational.
Prove by contrapositive
I believe the contrapositive is if x is rational or y is rational, then xy is rational
How do I go about proving this?

Actually you got the contrapositive slightly (but significantly) wrong.
The negation of $x$ irrational OR $y$ irrational is (both) $x$ AND $y$ are rational.
Can you proceed from this point? Just let $x = \frac ab, y = \frac cd$.
