Problem 7. Find an example of functions f and g such that f o g is a bijection, but g is not surjective and f is not injective. Prove that the functions you chose have the desired properties. [4 points] Problem 8. Let 4 and B be sets, and f: A B a function. Suppose 4; A and A3 C A are arbitrary subsets of A. Prove or disprove the following statements: (a) f(A1UAz) = f(A) U f(A2). [3 points] (b) f(A1 N Az) = f(A1) N f(A2). [3 points] Problem 9. Find the first five terms of the following sequences: (a) The sequence {a,} with a, = (-2)". [1 point] Assignment 3: Chapter 2 33 (b} The sequence {a,} with a, = 2. [1 point] {) The sequence {a, } with ay =2 and a, =4a,_, + 1. [1 point] (d) The sequence obtained by starting with 10 and obtaining each term by subtracting 7 from the previous term. [1 point] (e) The sequence whose first two terms are 1 and (-2), and each succeeding term is the product of the two previous terms. [1 point]