Each of the following functions f: Z × Z → Z is a closed binary operation on Z. Determine in each case whether f is commutative and/or associative.
(a) f(x, y) = x + y - xy
(b) f(x,y) = max{x, y}, the maximum (or larger) of x, y
(c) f(x, y) = xy
(d) f(x, y) = x + y - 3