For all x, there exists a y such that, .

My attempt at the solution:

Assuming x=/= y,

x|z can be written as xk=z

y|z can be written as yk=z

xk=yk

x=y

Therefore, the statement is false.

I have been told this solution is wrong. Can someone please tell me what I did wrong or give me a suggestion how to go about proving this?

Thanks