Prove the following using a proof by contrapositive:. For every pair of real numbers x and y, if x is rational and xy is irrational, then y is irrational.
Let q = a/b and r = c/b be two rational numbers written in lowest terms. Let s = q+r and s = e. f written in lowest terms. Assume that s is not 0.
Prove or disprove the following two statements.
a. If b and d are odd, then f is odd.
b. If b and d are even, then f is even.