The Match Set of a Random Permutation has the FKG Property

We prove a conjecture of Kumar Joang-Dev that if M = M(Sigma) = {i:Sigma(i) =i} is the (random) match set, or set of fixed points, of a random permutation Sigma of 1,2,..., n then f(M) and g(M) are correlated whenever f and g are increasing real-valued set functions of 2{1,...,n}, i.e. Ef(M)g(M)Eg(M).