Discrete Mathematics教学习题（华南理工）Tutorial07-Answer.pdfVIP

Discrete Mathematics I (Semester 2, 2013-2014) Tutorial 07 - Answer Refer to Chapter 5.1, 5.2, 5.3 Date: April-2014 1. List the ordered pairs in the relation R from A = {0,1,2,3,4} to B = {0,1,2,3}, where (a,b) ∈ R if and only if a) a = b b) a + b = 4 c) ab Answer: a) {(0,0), (1,1), (2,2), (3,3)} b) {(1,3), (2,2), (3,1), (4,0)} c) {(1,0), (2, 0), (3,0), (4,0), (2,1), (3,1), (4, 1), (3,2), (4,2), (4,3)} 2. Draw the directed graph and matrix for the following relation: a) {(a,b), (a,c), (b,c), (c,b)} on the set A = {a, b, c} b) {(a, a), (a, b), (b, a), (b, b), (c, c), (c, a), (c, d), (d, d)} on the set A = {a, b, c, d} Answer: a) 0 1 1   0 0 1  0 1 0    b) Discrete Mathematics I – Tutorial 7 1 1 1 0 0   1 1 0 0  1 0 1 1    0 0 0 1 3. Let R and R be relations on a set A represented by the matrices 1 2 0 1 1 0 1 0     M = 1 1 0 and M = 0 0 1 R R 1   2   1 0 1  1 1 0      Find the matrices that represent a) R2-1 b) R1 c) R1 U R2 d) R ⊕⊕ R