Use the following definitions. Let U be a universal set and let X ⊆ U. DefineWe call CX th...

Use the following definitions. Let U be a universal set and let X ⊆ U. Define

We call CX the characteristic function of X (in U). (A look ahead at the next Problem-Solving Corner may help in understanding the following exercises)

Prove that CX∩Y(x) = Cx(x) + CY(x) -CX(x)CY(x) for all XεU.