1.Suppose x and y are real numbers. Prove or give a counterexample.

if x + y is irrational, the x is irrational or y is irrational.

I found a counterexample already in a earlier question that asked if x is irrational and y is irrational, then x + y is irrational, but im not sure how to approach this question.

2.If x is a real number, then implies that

for this one, im not sure how to deal with the absolute value.

Thanks