// Discrete Math

(30 points total + 2 points bonus) 3. Let A-(a, b), B 3(x, y), and C-(0,1). [ each problem 2points) 8 points total Find a)A x B x C c) (B x B) U (C x A) d) (B) UA) where s* denotes power set 4 Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms of A and B. [ 2 points each] 8 points total a) the set of sophomores taking discrete mathematics in your school b) the set of sophomores at your school who are not taking discrete mathematics c) the set of students at your school who either are sophomores or are taking discrete mathematics d) the set of students at your school who either are not sophomores or are not taking discrete mathematics (bonus problem) 5. Given the set A 3( 1, 2, 3, 4, 5, 6). B-12, 3, 6, 7), C 3(3, 6, 9, 10), show the Venn diagram, and highlight/shade the following (Venn diagram 2 points, shading 2 points each)- six points total a) (Au B) (AnC) b) (A- B)n (A C) c) For the universal set U 1, 2, 3, 4, 5, 6, 7, 8, 9, 20). Express (2, 3, 6, 7) using bit string such that ith location is 0 if the element is missing in the set, and is '1' if it is present. (2 bonus points) 6. Show the following equivalences either using Venn Diagram or using transformation using various laws (2 points each) 8 points total a) A BE (A u B)- (An B) b) complement(A u B) complement(A) n complement(B) (De Morgan's law of sets) c) (A - B)-C- (A- B) n (A - C) d) A u (B n C) (A u B) n (A U C) (Distributive Law of sets)