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 Sn be the transposition (x y). Define

W = { Sn | (x) > (y) },

Z = { Sn | (x) < (y) }.

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