Statement: For every rational number z and every irrational number x, there exists a unique irrational number y such that z=x+y.

Write its negation, contrapositive and converse. Simple enough right? NOT SO, according to my teacher.

I think whats messing me up is "For every rational number z and every irrational number x" in the beginning.

Anyone wanna take a crack at it? And can someone give me examples similar to this one?