Suppose that A is a set, and fC Ax A is a relation on A such that f is symmetric f is a function Prove that f is a bijection of A with itself, that is, prove that f is both injective and surjective. (Hint: recall that a relation f C Ax A is a function iff (i) (Va e A)(3b € A)[(a, b) E f] (ii) if (a, b) E ƒ ^ (a, c) e f, then b= c.)

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