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

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 )

Find a formula for CXΔY (X Δ Y is the difference of X and Y ). The definition is given before Exercise Section 1.1)

Exercise

A binary operator f on a set X is commutative if f(x, y) = f(y, x) for all x, y ϵ X. state whether the given function f is a binary operator on the set X. If f is not a binary operator, state why. State whether or not each binary operator is commutative.

  f(x, y)= x − y,  X = {1,2,...}