Hey guys, just a bit lost with this proof

Let x and y be distinct numbers in the set {1, 2, . . . , n}, (n positive integer) and let $\displaystyle \alpha \in$ Sn be the transposition (x y). Define

W = { $\displaystyle \beta \in$ Sn | $\displaystyle \beta$(x) > $\displaystyle \beta$(y) },

Z = { $\displaystyle \beta \in$ Sn | $\displaystyle \beta$(x) < $\displaystyle \beta$(y) }.

Prove that W and Z are complementary subsets of Sn and that f($\displaystyle \beta$) = $\displaystyle \beta\alpha$ defines a bijective function from W to Z.