Solved: Let S be a subset of a universal set U. The

Chapter 2, Problem 2.3.67

(choose chapter or problem)

Let S be a subset of a universal set U. The characteristic function fs of S is the function from U to the set to, 1} such that fs(x) = 1 if x belongs to S and fsex) = 0 if x does not belong to S. Let A and B be sets. Show that for all x, a) hnB eX) = hex) . fB eX) b) hUB (X) = hex) + /Hex) - fA(X) . /Hex) c) hex) = 1 - fA(X) d) fAEBB (X) = fAeX) + fB eX) - 2h(x)fB eX)