Let X be any set, A C X. Define the characteristic function of A, XA : X → {0,1} as follows:
XA (x) = {1 if x E A
0 if x E/ A
Prove that:
(a) XA = 0 on X if and only if A = 0
(b) Xa = 1– XA
(c) XA A B = IXA - XB|