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## Homework Statement

Prove: For every rational number z, there exists irrational numbers x and y such that x + y = z.

## Homework Equations

by definition, a rational number can be represented by ratio of two integers, p/q.

## The Attempt at a Solution

Is there a way to do this by contraposition?

Would the contraposition be, For all rational numbers x and y, there does not exist an irrational number z such that x + y = z? I can handle from there, but I don't think my contraposition is correct.