MAT 299 Module 6 Quiz SNHU MAT299 Page 1 of 2 Module 6 Quiz MAT 299 Module 6 Quiz 1. (20 points) Suppose that x2y + xy2 + y3 = x3: a) Using the method of proof by contrapositive, show that if x and y are not both zero, then y 0. b) Using the method of proof by contradiction, show that if x and y are not both zero, then y 0. 2. (20 points) Prove the following two statements: a) For every integer n, 72 | n iff 8 | n and 9 | n. b) It is not true that for every integer n, 90 | n iff 6 | n and 15 | n. 3. (20 points) Let a, b, and c be real numbers with a 0. Prove that lim xc (ax + b) = ac + b. 4. (20 points) Suppose that {Ai | i I} is an indexed family of sets and B is a set. Prove that (iI Ai) B = iI (Ai B). 5. (20 points) Suppose R is a partial order on A and S is a partial order on B. Define a relation T on A B such that (a1, b1) T (a2, b2) iff a1 R a2 and b1 S b2. Is T a partial order on A x B? Either provide a proof to show that this is true or provide a counterexample to show that this is false. SNHU MAT299 Page 2 of 2 Module 6 Quiz