DISCRETE STRUCTURES

(a) Is f(x) = 8x3 , where f: Z Z, a bijection? Justify your answer.

(b) Let f and g be bijections, f: S T and g: T U. Then f-1 and g-1 exist. Also g f is a bijection, g f: S U. Show that (g f)-1 = f-1 g-1.

(c) Let f = (1 2 3) and g = (3 2 4) be permutations on set S = {1, 2, 3, 4}. Give the cyclic notation of the function f g.