# SET THEORY MATH 105

Exam #2 SET THEORY MATH 105 Name_______________________________________________ Section __________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. List the elements in the set. 1) {x | x is a counting number multiple of 2} A) B) {4, 6, 8, …} 2) { x C) {2, 4, 6, …} x is an even integer smaller than 8} A) {…, -6, -4, -2, 0, 2, 4, 6} C) {0, 2, 4, 6} B) {x | x is an integer between 16 and 21} D) {17, 18, 19, 20} 4) {9, 12, 15, 18, …, 39} A) {x | x is a multiple of 3} C) {x | x is a multiple of 3 between 6 and 42} B) {x | x is a multiple of 3 greater than 9} D) {x | x is a multiple of 3 between 9 and 39} Find n(A) for the set. 5) A = {x | x is a number on a clock face} A) n(A) = 12 B) n(A) = 3 B) n(A) = 10 1) 2) B) {…, -6, -4, -2, 2, 4, 6} D) {2, 4, 6} Write the set in set-builder notation. 3) {17, 18, 19, 20} A) {x | x is an integer less than 21} C) {x | x is an integer between 17 and 20} 6) A = {3, 3, 4, 4, …, 7, 7} A) n(A) = 3 D) {0, 2, 4, 6, …} C) n(A) = 24 D) n(A) = 6 C) n(A) = 5 D) n(A) = 6 3) 4) 5) 6) Write true or false for the following statement. Let A = {3, 5, 7, 9, 11, 13} B = {3, 5, 9, 11} C = {5, 9, 13} 7) Every element of B is also an element of C. A) True B) False 8) A = {x | x is an odd counting number greater than 1 and less than 15} A) True B) False 1 7) 8) Determine whether the statement is true or false. Let A = {1, 3, 5, 7} B = {5, 6, 7, 8} C = {5, 8} D = {2, 5, 8} U = {1, 2, 3, 4, 5, 6, 7, 8} 9) C D A) True B) False 10) C A A) True B) False 9) 10) Find the number of subsets of the set. 11) {math, English, history, science, art} A) 16 B) 24 C) 32 D) 28 Find the number of proper subsets of the set. 12) {poetry, drama, speech, art, film} A) 31 B) 24 C) 32 D) 16 Let U = {1, 2, 4, 5, a, b, c, d, e}. Find the complement of the set. 13) A = {2, 4, b, d} A) {1, 2, 4, 5, a, b, c, d, e} C) {1, 5, a, c, e} B) {1, 5, a, e} D) {1, 3, 5, a, c, e} 14) S = A) ‘ B) {0} C) Solve the problem. 15) List all possible subsets of the set {m, n}. A) {m}, {n}, C) {m}, {n}, {m, n} B) {m}, {n} D) {m}, {n}, {m, n}, 11) 12) 13) D) U 14) 15) List the elements in the set . Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. 16) A C A) {q, s, u, v, w, y, z} C) {q, s, u, w, y, v, w, x, y, z} B) {w, y} D) {q, s, u, v, w, x, y, z} 17) A’ B A) {s, u, w} C) {q, s, t, u, v, w, x, y} B) {q, r, s, t, v, x, y, z} D) {r, s, t, u, v, w, x, z} 2 16) 17) 18) B C A) {q, s, v, w, x, y, z} C) {y} 18) B) {y, z} D) {w, y, z} 19) A B’ A) {q, s, t, u, v, w, x, y} C) {r, s, t, u, v, w, x, z} 19) B) {u, w} D) {t, v, x} 20) A’ – C A) {q, s, u, v, x, z} B) {q, s, u} C) {r, t} D) {v, x, z} 21) A (B C) A) {q, w, y} B) {q, s, u, w, y, z} C) {q, y, z} D) {q, r, w, y, z} 22) B (A – C) A) {q, r, s, t, u, v, w, x, y} C) {q, s, u, y, z} B) {q, s} D) {q, s, u, y} For the given sets, construct a Venn diagram and place the elements in the proper region. 23) Let U = {c, d, g, h, k, u, q} A = {d, h, g, q} B = {c, d, h, u} A) B) C) D) 3 20) 21) 22) 23) 24) U = {2, 4, 6, 8, 10, 12} A = {2, 6, 10} B = {2, 4, 8} C = {2, 8, 10, 12} 24) A) B) C) D) 4 Solve the problem. 25) A survey of a group of 112 tourists was taken in St. Louis. The survey showed the following: 63 of the tourists plan to visit Gateway Arch; 44 plan to visit the zoo; 9 plan to visit the Art Museum and the zoo, but not the gateway Arch; 14 plan to visit the Art Museum and the Gateway Arch, but not the zoo; 16 plan to visit the Gateway Arch and the zoo, but not the Art Museum; 7 plan to visit the Art Museum, the zoo, and the Gateway Arch; 14 plan to visit none of the three places. How many plan to visit the Art Museum only? A) 44 B) 14 C) 98 5 D) 32 25)
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