Often in binary classification we are interested in the differences in the output of our current classifier, g, and an unknown function f that we are trying to learn. It is common in these cases to examine the quantity produced by f(x)g(x) for a given input x. For this problem, let D be an arbitrary distribution on the domain {−1, 1}n, and let f, g : {−1, 1}n -> {−1, 1} be two Boolean functions. (a) [6 points] Prove that Px∼D[f(x) ̸= g(x)] = 1 − Ex∼D[f(x)g(x)] 2 .