Prove that A (B C) = (A B) (A C)) by giving a Venn diagram proof. What is the Cartesian product of A={a, b, c, d} and B= {1, 4, 5}? Show that B Times A is not equal to A Times B, where A and B are as specified above Let A = {0,2,4,6,8,10}, B = {0, 1,2,3,4, 5,6}, and C = {4, 5,6, 7,8,9, 10}. Find A B C A B C Let A = {1, 2, 3, 4, 5} and B = {0, 3, 6} Find A - B B - A Use a membership table to show that A (B C) = (A B) (A C). Determine whether each of these functions from {a, b, c, d} to itself is one-to-one f(a)=b, f(b)=a, f(c) = c, f(d) = d Let f_1 and f_2 be functions from R to R such that f_1(x) = x_1 + x_2 and f_2(x) = x^2. What are the functions f_1 + f_2 and f_1 f_2? Suppose G: A rightarrow B and f: B rightarrow C where A = {1, 2, 3, 4}, B = { a, b, c}, C = {2, 8, 10}, and g and f are defined by g = {(1, b), (2, a), (3, b), (4, a)} and f = {(a, 8,), (b, 10), (c, 2)}. Find f g and f^-1. Let f and g be the functions from the set of integers to the set of integers defined by f(x) = 3x + 5 and g(x) = 5 - 9x. What is the composition of f and g? What is the composition of g and f