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