Ministry of Higher Education Kingdom of Saudi Arabia CSTS SEU, KSA Discrete Mathematics (Math 150) Level III, Assignment 2 (2015) 1. State whether the following statements are true or false: [9] (a) Two sets are equal if and only if they have the same number of elements. (a) (b) If A is a proper subset of B then the cardinality of A and B are same. (b) (c) If two sets are disjoint then their intersection is not an empty set. (c) (d) If range and codomain of a function f are equal then f is a surjective function. (d) (e) If f is not bijective then f can not be invertible. (e) (f) In an algorithm, innite number of steps may be used to get the desired output. (f) (g) If a 24-hour clock read 18:00, then after 95 hours it will read 17:00. (g) (h) Every prime number is not even. (h) (i) The integers 12, 17 and 21 are pairwise relatively prime number. (i) Page 1 of 3 Please go on to the next page. . . Math 150 Department of Mathematics 2. Select one of the alternatives from the following questions as your answer. (a) If A = {1, 7, 9, 15} then the number of possible subsets of A are A. 12 B. 16 C. 8 D. 6 (b) If A = {1, 3, 5, 7, 9, . . .} with the set of positive integers as the universal set. Then A is A. Set of positive even integers B. Set of negative even integers C. Set of negative integers D. None (c) If f : A B be a function such that f (a) = 4, f (b) = 1, f (c) = 2 and f (d) = 5 where A = {a, b, c, d, } and B = {1, 2, 3, 4, 5, 6} then A. f is 1-1 and onto both. B. f is onto but not 1-1. C. f is 1-1 but not onto. D. f is not a function. (d) If f : A B, g : B B and h : B A are functions then composition function gof be a function from A. A A B. B A C. B B D. A B (e) If f : Z Z be a function such that f (x) = 2x, then A. f is 1-1. B. f is onto C. f is bijective D. All of the above 7 (f) The value of (1)j is j=4 A. 0 B. 1 C. -1 Page 2 of 3 Please go on to the next page. . . [9] Math 150 Department of Mathematics D. 2 (g) Which of A. B. C. D. the following is NOT true: 12 4( mod 2) 17 7( mod 10) 104 91( mod 12) 210 10( mod 5) (h) The value of the modular expression (7 +11 10) .11 (9 +11 6) A. 255 B. 2 C. 4 D. 6 (i) If G.C.D(a, b) = 10 and ab = 40 then L.C.M (a, b) = A. 400 1 B. 4 C. 4 D. 1 3. If A = {1, 2, 3, 7, 9, 11, 14, 15, 16}, B = {1, 7, 11, 13, 19} and C = {2, 4, 6, 8, 10, 11, 12, 19}, then show that A (B C) = (A B) (A C). [2] 4. If f, g : Z Z be functions such that f (x) = 3x + 2 and g(x) = 2x2 + 1, then nd the values of (gof )(x) and (f og)(x). [2] 5. If an = an1 + an2 with a0 = 1, and a1 = 2, then nd the value of a5 of the given sequence. [2] 6. List all the steps used to search for 9 in the sequence 1,3,4,5,6,8,9,11 using linear search. 7. Find the octal expansion of (765)10 . [2] 8. Find the greatest common divisor of 314 and 520 by using the Euclidean Algorithm. [2] Page 3 of 3 End of Assignment