Let S be a subset of a universal set U. The characteristic function fS of S is the function f : U -> {0, 1} defined by fS(x) = 1 if x is in S and fS(x) = 0 if x is not in S. So for example, if U = {0, 1, 2, 3} and S = {0, 3} then fS(0) = 1, fS(1) = 0, fS(2) = 0, and fS(3) = 1.
Let A ⊆ U and B ⊆ U. Show that fA ∩ B(x) = fA(x) · fB(x).