12. Let f : X - Y and g : Y - Z. Which of the following statements is not true? (A) If f and g are both 1 - 1 then so is go f. (B) If f and g are both onto then so is go f. C) If go f is 1 - 1, then both f and g are 1 - 1. D) If go f is onto, then g is onto, but f need not be. 13. If you are asked to prove the statement "for every prime number p, vp is irrational" by contradiction, with which of the following sentences should you begin the proof? (A) We suppose that for a specific prime p there is q E Q a rational such that vp = q; let p be 2. (B) For some prime p, suppose there are integers a, b E Z such that b / 0 and Vp = :. (C) For some prime p, suppose vp is irrational but for all primes q # p, q is rational; we will show that Vp must be rational as well. (D) For all primes p > 2, suppose that vp is irrational but v2 = ; for some integers a, b E Z such that 6 0 . 14. The greatest common divisor of 48 and 30 is (A) 2. (B) 4. (C) 6. (D) 8. 15. Suppose that the powerset of a set X is the following set: P(X) = 10, {0}, {0}, (1}, {0, 0}, {0, 1}, (0, 1}, (0, 0, 1} } Which of the following is the set X ? (A) {0, 1} (B) {0, 0, 1} (C) {0, {0}, 10}, (1} } (D) {{0}, 0, 1} is true? 16. If m, p, q, k, l E N with m 2 3, and p = q modulo m, and if k = ( modulo m, then which of these statements (A) pk = ql modulo m. (B) p+ q= k + l modulo m. (C) p2 + 92 = k2 + 12 modulo m. (D) p - k = 1 modulo m. 17. If A and B are sets, what does A = B mean? (A) There is a bijection between A and B. (B) The elements of A and B are in one-to-one correspondence. (C) Every element of A is also an element of B. (D) If r E A then I E B, and if x E B then x E A. 18. Which of the following sets is equal to An (BnC) ? (A) (An B) U(And) (B) AnBAC C) (AnB)n( And) (D) (An B) U (And)