For each the following groups of sets, determine whether they form a partition for the set of integers. Explain your answer. a. A1 = {n Z : n > 0} A2 = {n Z : n < 0} b. B1 = {n Z : n = 2k, for some integer k} B2 = {n Z : n = 2k + 1, for some integer k} B3 = {n Z : n = 3k, for some integer k} 2. (10 pts, 4 parts 2.5 points each) Define f: Z Z by the rule f(x) = 6x + 1, for all integers x. a. Is f onto? b. Is f one-to-one? c. Is it a one-to-one correspondence? d. Find the range of f. Explain each of your answers. 3. (10 pts, 2 parts 5 points each) f: R R and g: R R are defined by the rules: f(x) = x2 + 2 x R g(y) = 2y + 3 y R Find f g and g f