1. The problem statement, all variables and given/known data Relation is x^y = y^x........x and y belong to integers 2. Relevant equations 3. The attempt at a solution Well i have already proven that they are reflexive and symmetric. I have doubt with transitive I did the follwoing way x^y = y^x.......(1) and y^z = z^y.........(2) from(1) x^z = y^(zx/y) from(2) z^x = y^(zx/y) Therefore x^z = z^x proving it is transitive But the test paper solution does it this way from(1) y = x^(y/x) and from(2) y = z^(y/z) Now x^(y/x) = z^(y/z) ..... so its not transitive Which is correct? Did i do anything wrong?