# Introductory Discrete Mathematics

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Introductory Discrete Mathematics Page 42 1. List the (distinct) elements in each of the following sets: {x Z | xy = 15 for y Z}Solution: C = { 1, 3, 5, 15, -1, -3, -5, -15} (both positive and negative of 15) e. {a N | a <-4 and a >a} Solution:It is impossible to list the elements since they are infinite in number. “N” refers to natural numbers and therefore "-4" is irrelevant. 2. List five elements in each of the following sets: d. {nN|n2 + n is a multiple of 3} Solution:The numbers are in the form n2+n=3p for some integer P hence: n={3,5,6,8,9} 9a. List all the subsets of the set {a, b, c, d} that contain Solution i.) four elements - {a,b,c,d}ii.) three elements - {a,b,c}, {a,b,d}, {a,c,d}, {b,c,d}iii.) two elements - {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}iv.) one element - {a}, {b}, {c}, {d}v.) no elements - {0} Page 49 3. Let A = {(-1,2), (4, 5), (0, 0), (6, -5), (5, 1), (4, 3)}. a. {a + b | (a, b) A} Solution: A = {1, 9, 0, 6, 7}. b. {a | a >0 and (a, b) A for some b} Solution:{4,6,5,4} 4. List the elements in the sets A = {(a, b) N x N|a < b, b < 3 } and B = {a/b | a, b {-1, 1, 2} }. Solution:A = {(1,1), (1,2), (1,3), (2,2), (2,3), (3,3)} Solution:B = {(1,2), (2,1),(1,-1)} 10. (Explain your answers) The universal set for this problem is the set of students attending Miskatomic University. Using only the set theoretical notation we have introduced in this chapter, rewrite each of the following assertions. Solutions Computer science majors had a test on Friday. CS⊆TNo math major ate pizza last Thursday. M∩P=∅ Since M∩P ate Pizza last Thursday. Some math majors did not eat pizza last Thursday. is M∩Pc≠∅ Since M∩Pc did not eat Pizza

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