Review Test 1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is true or false. 1) 4 ∈ {1, 2, 3, ..., 15} 1) A) True B) False 2) 21 ∉ {1, 2, 3, ..., 40} 2) A) True B) False 3) 19 ∈ {2, 4, 6, ..., 20} 3) A) True B) False Fill in the blank with either ∈ or ∉ to make the statement true. 4) Saskatchewan _____ the set of states in the United States 4) A) ∈ B) ∉ Find the cardinal number for the set. 5) {27, 29, 31, 33, 35} 5) A) 5 B) 27 C) 4 D) 6 6) Determine the cardinal number of the set {x | x is a letter of the alphabet} 6) A) 23 B) 26 C) 30 D) 25 Are the sets equivalent? 7) A = {23, 25, 27, 29, 31} 7) B = {24, 26, 28, 30, 32} A) Yes B) No 8) A = {13, 14, 14, 15, 15, 15, 16, 16, 16, 16} 8) B = {16, 15, 14, 13} A) Yes B) No Are the sets equal? 9) {50, 52, 54, 56, 58} = {52, 54, 56, 58} 9) A) Yes B) No 10) A is the set of residents age 26 or older living in the United States 10) B is the set of residents age 26 or older registered to vote in the United States A) Yes B) No 11) A = {18, 19, 19, 20, 20, 20, 21, 21, 21, 21} 11) B = {21, 20, 19, 18} A) Yes B) No 12) A = {14, 15, 16, 17, 18} 12) B = {13, 14, 15, 16, 17} A) Yes B) No 1 Write ⊆ or ⊈ in the blank so that the resulting statement is true. 13) {4, 34, 39} {15, 34, 39, 49} 13) A) ⊆ B) ⊈ 14) {c, a, n, d, i, d, a, t, e} _____ {a, c, d, e, i, t, a, n, d} 14) A) ⊆ B) ⊈ Determine whether the statement is true or false. 15) ∅ ⊆ {France, Germany, Switzerland} 15) A) True B) False Use ⊆, ⊈, ⊂, or both ⊂ and ⊆ to make a true statement. 16) {a, b} {z, a, y, b, x, c} 16) A) ⊂ and ⊆ B) ⊈ C) ⊂ D) ⊆ List all the subsets of the given set. 17) {8} 17) A) {0}, {8}, { }B){ } C) {8} D) {8}, { } Calculate the number of subsets and the number of proper subsets for the set. 1 1 1 1 18) , , , 18) 6 7 8 9 A) 15; 14 B) 14; 15 C) 16; 15 D) 15; 16 19) {1, 3, 5, 7, 9, 11} 19) A) 64; 63 B) 63; 62 C) 63; 64 D) 62; 63 20) {x | x is a day of the week} 20) A) 127; 126 B) 64; 65 C) 128; 127 D) 128; 129 2 Place the various elements in the proper regions of the Venn diagram. 21) Let U = {8, 9, 10, 11, 12, 13, 14} and A = {8, 9, 12}. Find Aʹ and place the elements in the proper 21) region. A) Aʹ = {11, 12, 13, 14} B) Aʹ = {8, 9, 10, 11, 12, 13, 14} C) Aʹ = {8, 9, 12} D) Aʹ = {10, 11, 13, 14} Use the Venn diagram to list the elements of the set in roster form. 22) List the elements of A. 22) A) {11, 13, 14, 17} B) {12, 15, 16} C) {11, 12, 13} D) {13, 17} 3 23) List the elements of U. 23) A) {11, 14} B) {13, 17} C) {12, 15, 16} D) {11, 12, 13, 14, 15, 16, 17, 18, 19} Let U = {1, 2, 4, 5, a, b, c, d, e}. Use the roster method to write the complement of the set. 24) A = {2, 4, b, d} 24) A) {1, 2, 4, 5, a, b, c, d, e} B) {1, 5, a, c, e} C) {1, 5, a, e} D) {1, 3, 5, a, c, e} Let U = {21, 22, 23, ..., 40}, A = {21, 22, 23, 24, 25}, B = {26, 27, 28, 29}, C = {21, 23, 25, 27, ..., 39}, and D = {22, 24, 26, 28, ..., 40}. Use the roster method to write the following set. 25) Aʹ 25) A) Aʹ = {21, 22, 23, . , 40} B) Aʹ = {27, 29, 31, . , 39} C) Aʹ = {26, 28, 30, . , 40} D) Aʹ = {26, 27, 28, . , 40} Let U = {21, 22, 23, 24, ...}, A = {21, 22, 23, 24, ..., 40}, B = {21, 22, 23, 24, ..., 50}, C = {22, 24, 26, 28, ...}, and D = {21, 23, 25, 27, ...}. Use the roster method to write the following set. 26) Cʹ 26) A) Cʹ = {21, 22, 23, 24, ...} B) Cʹ = {21, 23, 25, 27, ..., 39} C) Cʹ = {21, 23, 25, 27, ...} D) Cʹ = {22, 24, 26, 28, ...} Solve the problem. 27) If the universal set is the set of the days of the week and set A is the set of days that begin with the 27) letter T, write Aʹ using the roster method. Describe Aʹ in words. A) Aʹ = {Sunday, Monday, Friday, Saturday}; Aʹ is the days of the week that do not begin with the letter T. B) Aʹ = {Tuesday, Thursday}; Aʹ is the days of the week that begin with the letter T. C) Aʹ = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}; Aʹ is the days of the week that do not begin with the letter T. D) Aʹ = {Sunday, Monday, Wednesday, Friday, Saturday}; Aʹ is the days of the week that do not begin with the letter T. 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}. List the elements in the set. 28) A ∩ Bʹ 28) A) {r, s, t, u, v, w, x, z} B) {t, v, x} C) {u, w} D) {q, s, t, u, v, w, x, y} 4 29) (A ∩ B)ʹ 29) A) {q, s, t, u, v, w, x, y} B) {s, u, w} C) {r, t, u, v, w, x, z} D) {t, v, x} 30) A ∩ B 30) A) {q, s, y} B) {q, s, u, w, y, z} C) {v, w, x, y, z} D) {r, t, u, v, w, x, z} 31) (A ∪ B)ʹ 31) A) {s, u, w} B) {r, s, t, u, v, w, x, z} C) {r, t, v, x} D) {t, v, x} 32) B ∪ C 32) A) {q, r, s, t, u, v, w, x, y, z} B) {q, s, u, w, y} C) {v, w, x, y, z} D) {q, s, v, w, x, y, z} 33) B ∪ U 33) A) {q, s, u, w, y} B) {q, s, y, z} C) {v, w, x, y, z} D) {q, r, s, t, u, v, w, x, y, z} 34) A ∩ Bʹ 34) A) {r, s, t, u, v, w, x, z} B) {u, w} C) {q, s, t, u, v, w, x, y} D) {t, v, x} 35) Cʹ ∪ Aʹ 35) A) {w, y} B) {q, r, s, t, u, v, x, z} C) {s, t} D) {q, s, u, v, w, x, y, z} 36) B ∪ C 36) A) {q, s, v, w, x, y, z} B) {v, w, x, y, z} C) {q, r, s, t, u, v, w, x, y, z} D) {q, s, u, w, y} 37) (A ∩ C)ʹ 37) A) {w, y} B) {q, r, s, t, u, v, x, z} C) {q, r, s, t, u, v, w, x, y, z} D) {q, s, y, z} 38) C ∪ ∅ 38) A) { } B) {q, s, y, z} C) {v, w, x, y, z} D) {q, s, u, w, y} 39) B ∪ U 39) A) {v, w, x, y, z} B) {q, r, s, t, u, v, w, x, y, z} C) {q, s, u, w, y} D) {q, s, y, z} 5 Use the Venn diagram to list the elements of the set in roster form. 40) 40) A ∪ B A) {11, 12, 14, 15, 16} B) {13, 17} C) {11, 12, 13, 14, 15, 16, 17, 18, 19} D) {11, 12, 13, 14, 15, 16, 17} 41) 41) Aʹ A) {12, 15, 16, 18, 19} B) {11, 13, 14, 17} C) {12, 15, 16} D) {11, 14, 18, 19} 42) 42) (A ∩ B)ʹ A) {18, 19} B) {11, 12, 14, 15, 16} C) {11, 12, 14, 15, 16, 18, 19} D) {13, 17} 6 43) 43) (A ∪ B)ʹ A) {11, 12, 14, 15, 16} B) {11, 12, 13, 14, 15, 16, 17} C) {18, 19} D) {13, 17} Use sets to solve the problem. 44) Results of a survey of fifty students indicate that 30 like red jelly beans, 29 like green jelly beans, 44) and 17 like both red and green jelly beans. How many of the students surveyed like no green jelly beans? A) 38 B) 17 C) 30 D) 21 45) Monticello residents were surveyed concerning their preferences for candidates Moore and Allen 45) in an upcoming election. Of the 800 respondents, 300 support neither Moore nor Allen, 100 support both Moore and Allen, and 250 support only Moore. How many residents support Allen? A) 400 B) 100 C) 250 D) 150 Use the formula for the cardinal number of the union of two sets to solve the problem. 46) Set A contains 35 elements and set B contains 22 elements. If there are 40 elements in (A ∪ B) then 46) how many elements are in (A ∩ B)? A) 13 B) 17 C) 5 D) 8 47) Set A contains 5 elements, set B contains 11 elements, and 3 elements are common to sets A and B.