Test Bank for Mathematical Ideas, 14th Edition

Exam Name___________________________________ 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 whole number between 3 and 7} 1) _______ A) {4, 5, 6} B) {4, 5, 6, 7} C) {3, 4, 5, 6, 7} D) {3, 4, 5, 6} 2) {x | x is an integer between -7 and -3} 2) _______ A) {-7, -6, -5, -4} B) {-6, -5, -4, -3} C) {-6, -5, -4} D) {-7, -6, -5, -4, -3} 3) {x | x is a negative multiple of 9} 3) _______ A) {0, -9, -18, …} B) {-9, -18, -27, …} C) {-9, -81, -729, …} D) {9, 18, 27, …} 4) {x | x is an integer greater than -6} 4) _______ A) {-5, -4, -3, …} B) {-7, -8, -9} C) {-5, -4, -3, -2} D) {-7, -8, -9, …} 5) The set of all whole numbers greater than 2 and less than 6 5) _______ A) {3, 4, 5, 6} B) {2, 3, 4, 5} C) {3, 4, 5} D) {2, 3, 4, 5, 6} 6) {x | x is a counting number multiple of 4} 6) _______ A) {4, 8, 12, …} B) {8, 12, 16, …} C) ∅ D) {0, 4, 8, 12, …} 7) {x | x is a counting number less than -1} 7) _______ A) {0, 1, 2, …} B) ∅ C) {-2, -3, -4, …} D) {…, -4, -3, -2} 8) The set of all positive integer powers of 3. 8) _______ A) {1, 3, 9, 27, 81, 243, …} B) {1, 8, 27, 64, 125, …} C) {3, 9, 27, 81, 243, …} D) {3, 6, 9, 12, 15, …} 9) { x is an even integer smaller than 8} A) {…, -6, -4, -2, 2, 4, 6} B) {2, 4, 6} C) {…, -6, -4, -2, 0, 2, 4, 6} D) {0, 2, 4, 6} 10) The set of the days of the week 10) ______ A) {Saturday, Sunday} B) {Friday, Monday, Saturday, Sunday, Thursday, Tuesday, Wednesday} C) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday} D) {Tuesday, Thursday} Write the set in set-builder notation. 11) {2} 11) ______ A) {x | x is a natural number} B) {x is a constant} C) {x} D) {x | x is the natural number 2} 12) {2, 4, 6, 8} 12) ______ A) {x | x is any even natural number} B) {2, 4, 6, 8} 9) _______ C) {x | x is any even integer less than 10} D) {x | x is an even natural number less than 10} 13) {16, 17, 18, 19} 13) ______ A) {x | x is an integer less than 20} B) {x | x is an integer between 16 and 19} C) {16, 17, 18, 19} D) {x | x is an integer between 15 and 20} 14) {-6, -5, -4, -3, …} 14) ______ A) {x | x is an integer greater than -7} B) {x | x is any integer} C) {-6, -5, -4, -3} D) {x | x is an integer between -7 and -2} 15) {…, -3, -2, -1, 0, 1, 2, 3, …} 15) ______ A) {x | x is an integer} B) {-3, -2, -1, 0, 1, 2, 3} C) {x | x is a natural number} D) {x | x is any integer greater than -3} 16) {12, 15, 18, 21, …, 42} 16) ______ A) {x | x is a multiple of 3 greater than 12} B) {x | x is a multiple of 3 between 9 and 45} C) {x | x is a multiple of 3 between 12 and 42} D) {x | x is a multiple of 3} 17) {-3, -1, 1, 3, 5, …} 17) ______ A) { x is an odd integer greater than -4} B) { x is an odd integer between -4 and 6} C) { x is an integer greater than -4} D) { x is an odd integer} 18) {2, 4, 8, 16, 32, …} 18) ______ A) { x is a positive multiple of 2} B) { x is an integer power of 2} C) { x is a positive multiple of 4} D) { x is a positive integer power of 2} 19) The set of all calculus books 19) ______ A) {x is a calculus book} B) {x | x is a calculus book} C) {any calculus book} D) {a calculus book} 20) The set of all cars owned by students 20) ______ A) {x | x is a student with a car} B) {x is a student with a car} C) {x | x is a car owned by a student} D) {x is a car} Identify the set as finite or infinite. 21) {9, 10, 11, …, 36} 21) ______ A) Infinite B) Finite 22) A) Finite 22) ______ B) Infinite 23) {x | x is a counting number larger than 136} 23) ______ A) Infinite B) Finite 24) {x | x is an odd counting number} A) Finite B) Infinite 24) ______ 25) {x | x is a 12-headed lizard} 25) ______ A) Infinite B) Finite 26) {x | x is a fraction between 63 and 64} A) Infinite B) Finite 27) {x | x is a prime number} A) Infinite B) Finite 27) ______ 28) 28) ______ A) Infinite 26) ______ B) Finite Find n(A) for the set. 29) A = {0, 2, 4, 6, 8} 29) ______ A) n(A) = 8 B) n(A) = 4 C) n(A) = 2 D) n(A) = 5 30) A = {700, 701, 702, …, 7000} 30) ______ A) n(A) = 4 B) n(A) = 7000 C) n(A) = 6301 D) n(A) = 6300 31) A = {x | x is a month in the year} 31) ______ A) n(A) = 12 B) n(A) = 52 C) n(A) = 1 D) n(A) = 24 32) A = {x | x is a number on a clock face} A) n(A) = 3 B) n(A) = 12 C) n(A) = 24 33) A = {x | x is a second in a minute} A) n(A) = 60 B) n(A) = Infinite 32) ______ D) n(A) = 6 33) ______ C) n(A) = 12 D) n(A) = 120 34) A = {1, 1, 2, 2, …, 5, 5} 34) ______ A) n(A) = 10 B) n(A) = 5 C) n(A) = 6 D) n(A) = 3 35) A = {-8, -7, -6, …, 0} 35) ______ A) n(A) = 4 B) n(A) = 1 C) n(A) = 9 D) n(A) = 8 36) A = A) n(A) = 31 36) ______ B) n(A) = Infinite 37) A = A) n(A) = Infinite C) n(A) = 29 D) n(A) = 30 37) ______ B) n(A) = 19 C) n(A) = 40 D) n(A) = 38 Determine whether or not the set is well defined. 38) {x | x is a tennis player who has won at Wimbledon} 38) ______ A) Not well defined B) Well defined 39) {x | x is a low-fat ice cream} 39) ______ A) Well defined B) Not well defined 40) {x | x is a football team that has won the Super Bowl} 40) ______ A) Well defined B) Not well defined 41) {x | x is a mystery book in the library} A) Well defined B) Not well defined 41) ______ 42) {x | x is a stock on the AmEx today} 42) ______ A) Not well defined B) Well defined 43) {x | x is an expensive boat on the Great Lakes} A) Well defined B) Not well defined 43) ______ 44) {x | x is a four-year college in Utah} 44) ______ A) Not well defined B) Well defined Complete the blank with either ∈ or ∉ to make the statement true. 45) -5 {5, 7, 9, …, 17} 45) ______ A) ∉ B) ∈ 46) 0 A) ∉ {-2, 2, 4, 18, 28} B) ∈ 46) ______ 47) {7} {{4}, {5}, {6}, {7}, {8}} 47) ______ A) ∈ B) ∉ 48) 4 A) ∉ {10, 9, 8, 7} B) ∈ 48) ______ 49) 8 A) ∉ {5, 10, 4, 8, 19} 49) ______ B) ∈ 50) 11 {9, 10, 11, 12} 50) ______ A) ∈ B) ∉ 51) a A) ∉ {A, B, C, …, Z} 51) ______ B) ∈ 52) 7 A) ∉ {2, 3, 4, …, 7} B) ∈ 52) ______ 53) {-5} {-4 – 3, -3 – 3, -2 – 3, -1 – 3} A) ∈ B) ∉ 53) ______ 54) 0 A) ∈ 54) ______ {1 + 5, -1 + 5, -3 + 5, -5 + 5} B) ∉ Tell whether the statement is true or false. 55) 10 ∈ {20, 30, 40, 50, 60} 55) ______ A) True B) False 56) {2, 10, 15} = {0, 2, 10, 15} A) True B) False 56) ______ 57) 17 ∉ {16, 14, 13, …, 1} 57) ______ A) True B) False 58) {8} = {x | x is an even counting number between 10 and 16} A) True B) False 59) {54, 55, 54, 55} = {54, 55} A) True B) False 59) ______ 60) {2, 16, 26, 9, 32} = {32, 16, 9, 62, 2} A) True B) False 60) ______ 61) {x | x is a counting number greater than 36} = {36, 37, 38, …} A) True B) False 62) 11 ∉ {x | x is an even counting number} A) True B) False 63) k ∉ {p, a, k, h, v} A) True B) False 58) ______ 61) ______ 62) ______ 63) ______ 64) {s, q, y, o, d} = {o, d, q, s, y} A) True B) False 64) ______ 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} 65) 5 ∉ C 65) ______ A) True B) False 66) 9 ∈ B 66) ______ A) True B) False 67) Every element of B is also an element of C. A) True B) False 67) ______ 68) A = {x | x is an odd counting number greater than 1 and less than 15} 68) ______ A) True B) False 69) 0 ∈ A 69) ______ A) True B) False 70) Every element of C is also an element of A. A) True B) False 70) ______ 71) {x | x is an odd counting number less than 15} = A A) True B) False 71) ______ 72) {13} ∈ B 72) ______ A) True B) False Use ⊆ or ⊈ in the blank to make a true statement. 73) {4, 6, 8} {3, 4, 5, 6, 8} 73) ______ A) ⊈ B) ⊆ 74) {3, 31, 36} A) ⊆ B) ⊈ {16, 31, 36, 46} 75) {a, c, g, i} A) ⊆ B) ⊈ {a, c, g, i, k} 76) ∅ A) ⊆ ∅ B) ⊈ 74) ______ 75) ______ 76) ______ 77) {7, 9, 11} A) ⊈ B) ⊆ {x | x is an odd counting number} 78) {k, p, d} A) ⊆ B) ⊈ {k, k, p, p, d, d}78) ______ 79) {x | x is a counting number larger than 5} A) ⊆ B) ⊈ 77) ______ {7, 8, 9, …} 79) ______ Decide whether ⊆, ⊂, both, or neither can be placed in the blank to make a true statement. 80) {4, 5, 6} {3, 4, 5, 6} 80) ______ A) ⊆ B) Both ⊂ and ⊆C) ⊂ D) Neither 81) ∅ A) ⊆ {4, 19, 28, 43} 81) ______ B) Both ⊂ and ⊆C) Neither D) ⊂ 82) {4, 5, 6} {4, 5, 6} 82) ______ A) Both ⊂ and ⊆ B) ⊆ C) ⊂ D) Neither 83) {0} ∅ 83) ______ A) ⊆ B) Both ⊂ and ⊆C) Neither D) ⊂ 84) {a, b} {z, a, y, b, x, c} 84) ______ A) ⊂ B) Both ⊂ and ⊆C) Neither D) ⊆ 85) {s, r, t} {s, r, t} 85) ______ A) Both ⊆ and ⊂ B) Neither C) ⊆ D) ⊂ 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} 86) C ⊂ D 86) ______ A) True B) False 87) ∅ ⊆ A 87) ______ A) True B) False 88) {6, 5, 8, 7} ⊆ B A) True B) False 88) ______ 89) D ⊆ B 89) ______ A) True B) False 90) A ≠ {7, 5, 3, 1} A) True B) False 90) ______ 91) {5} ⊆ D 91) ______ A) True B) False 92) {0} ⊆ U 92) ______ A) True B) False 93) {8, 5, 2} ⊂ D 93) ______ A) True B) False 94) C ⊈ B 94) ______ A) True B) False 95) C ⊈ A 95) ______ A) True B) False Find the number of subsets of the set. 96) {7, 8, 9} 96) ______ A) 6 B) 8 C) 7 D) 3 97) {x | x is an even number between 19 and 37} 97) ______ A) 512 B) 68 C) 256 D) 8 98) {0} 98) ______ A) 4 B) 2 C) 1 D) 0 99) {mom, dad, son, daughter} A) 14 B) 8 C) 12 D) 16 99) ______ 100) {math, English, history, science, art} 100) _____ A) 24 B) 16 C) 32 D) 28 101) {x | x is a day of the week} 101) _____ A) 256 B) 124 C) 128 D) 127 102) {1, 2, 3, …, 9} 102) _____ A) 16 B) 508 C) 1024 D) 512 Find the number of proper subsets of the set. 103) {5, 6, 7} 103) _____ A) 6 B) 2 C) 5 D) 7 104) {x | x is an even number between 17 and 29} A) 64 B) 28 C) 32 D) 63 105) {0} 105) _____ A) 0 B) 1 C) 2 104) _____ D) 4 106) {car, boat, truck, train} A) 15 B) 8 C) 16 D) 14 106) _____ 107) {poetry, drama, speech, art, film} A) 32 B) 31 C) 16 D) 24 107) _____ 108) {x | x is a day of the week} 108) _____ A) 64 B) 256 C) 128 D) 127 109) {1, 2, 3, …, 6} A) 63 B) 127 C) 64 109) _____ D) 58 Let U = {1, 2, 4, 5, a, b, c, d, e}. Find the complement of the set. 110) A = {2, 4, b, d} 110) _____ A) {1, 2, 4, 5, a, b, c, d, e} B) {1, 3, 5, a, c, e} C) {1, 5, a, e} D) {1, 5, a, c, e} 111) S = {1, 5, e, d, a} 111) _____ A) {2, 4, b, c} B) {2, 3, 4, a, b, c} 112) S = {1, 2, 4, 5, a, b, c, e} A) {d} B) {3, d} C) {u} D) ∅ 113) Q = {a, b, c, d} A) {e} B) {1, 2, 4, 5} C) {1, 2, 4, b, c} D) {2, 3, 4, b, c} 112) _____ 113) _____ C) {1, 2, 4, 5, e} D) {1, 2, 3, 4, 5, e} 114) G = {a} 114) _____ A) {u, v} B) {1, 2, 4, 5, b, c, d, e} C) {1, 2, 3, 4, 5, b, c, d, e} D) {1, 2, 5, b, c, d, e} 115) S = ∅ A) {0} B) U 115) _____ C) ∅ D) ∅’ 116) P = {a, b, d, e, 1, 2, 4, 5} 116) _____ A) U B) ∅ C) {c} D) {c, 3} 117) C = {1, 2, 5, b, d} 117) _____ A) {3, 4, a, b, c, e} B) {3, 4, a, c, e} C) {4, a, b, c, e} D) {4, a, c, e} 118) T = U 118) _____ A) U B) {U – T’} C) T D) ∅ 119) P = {e, a, c, 4, 5} 119) _____ A) {1, 2, b, c, d} B) {b, d, 1, 2, 3} C) {1, 2, b, d} D) {1, 2, 3, b, d} The lists below show five agricultural crops in Alabama, Arkansas, and Louisiana. Alabama soybeans (s) peanuts (p) corn (c) hay (h) wheat (w) Arkansas soybeans (s) rice (r) cotton (t) hay (h) wheat (w) Louisiana soybeans (s) sugarcane (n) rice (r) corn (c) cotton (t) Let U be the smallest possible universal set that includes all of the crops listed, and let A, K and L be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find each of the following sets. 120) The set of crops in U. 120) _____ A) {s, p, c, h, w, s, r, t, h, w, s, n, r, c, t} B) {s, p, c, w, r, t, n} C) {c, h, n, p, r, s, t, w} D) {s, p, c, h, w, r, t, n, c} 121) The set of crops in A’. 121) _____ A) {n, r, t} B) {c, h, n, r, s, t, w} C) {h, n, r, t} D) {r, t} 122) The set of crops in both A and K A) {c, h, p, r, s, t, w} B) {h, s, w} C) {c, p, r, t} D) {c, h, s, t, w} 122) _____ 123) The set of crops in both L and K A) {c, n, r, s, t} B) {r, s, t} C) {c, h, n, w} D) {c, h, n, r, s, t, w} 123) _____ 124) The set of crops in both L and K’ A) {c, n} B) {r, s, t} C) {h, w} 124) _____ D) {c, n, p} 125) The set of crops in both A and L’ 125) _____ A) {h, p, w} B) {n, r, t} C) {h, n, t, w} D) {c, s} 126) The set of crops in both A’ and K’ A) {n} B) {c, n, p, r, t} C) {c, p, r, t} 126) _____ D) ∅ 127) The set of crops common to A, K, and L A) {c, h, n, p, r, s, t, w} B) {n, p, s} C) {s} D) {n, p} 127) _____ 128) The set of crops in either A or L or both A) {c, h, n, p, r, s, t, w} B) {c, n, p} C) {h, n, p, r, t, w} D) {c,s} 128) _____ 129) The set of crops in either A’ or L or both 129) _____ A) {c, n, r, s, t} B) {h, n, p, r, t, w} C) {h, p, w} D) {n, r, t} Solve the problem. 130) List all possible subsets of the set {m, n}. 130) _____ A) {m}, {n} B) {m}, {n}, ∅ C) {m}, {n}, {m, n} D) {m}, {n}, {m, n}, ∅ 131) List all possible proper subsets of the set {2, 6, 7}. 131) _____ A) ∅, {2}, {6}, {7}, {2, 6}, {2, 7}, {6, 7} B) {2}, {6}, {7}, {2, 6}, {2, 7}, {6, 7}, {2, 6, 7} C) ∅, {2}, {6}, {7}, {2, 6}, {2, 7}, {6, 7}, {2, 6, 7} D) {2}, {6}, {7}, {2, 6}, {2, 7}, {6, 7} 132) A committee is to be formed. Possible candidates for the committee are Eric, Frances, Greg, and Jose. Denoting these four people by e, f, g, j, list all possible committees of two people (ie list all possible subsets of size two). 132) _____ A) {e, f}, {e, g}, {e, j}, {f, j}, {g, j} B) {e, f}, {e, g}, {f, g}, {g, j} C) {e, f}, {e, g}, {e, j}, {f, g}, {f, j}, {g, j}, {f, e}, {g, e} D) {e, f}, {e, g}, {e, j}, {f, g}, {f, j}, {g, j} 133) A committee is to be formed. Possible candidates for the committee are Eric, Frances, Greg, and Jose. Denoting these four people by e, f, g, j, list all possible committees if the committee is to contain at least two people and may contain up to four people. 133) _____ A) {e, f}, {e, g}, {e, j}, {f, g}, {f, j}, {g, j}, {e, f, g}, {e, f, j}, {e, g, j}, {f, g, j}, {e, f, g, j} B) {e, f}, {e, g}, {e, j}, {f, g}, {f, j}, {g, j}, {e, f, g}, {e, f, j}, {e, g, j}, {f, g, j} C) {e, f}, {e, g}, {e, j}, {f, g}, {f, j}, {g, j}, {e, f, g}, {e, f, j}, {f, g, j}, {e, f, g, j} D) {e, f}, {e, g}, {e, j}, {f, j}, {e, f, g}, {e, f, j}, {e, g, j}, {f, g, j}, {e, f, g, j} 134) An adventure travel company has reservations from four people (Lee, Maria, Nancy, and Pablo) for its white water rafting trip on June 1st. However the company knows that any of these people may fail to show up on the day of the trip. Denoting these four people by l, m, n, p, list all possibilities for the group of people who show up on June 1st for the rafting trip (ie list all possible subsets of 134) _____ A) {l}, {m}, {n}, {p}, {l, m}, {l, n}, {l, p}, {m, n}, {m, p}, {n, p}, {l, m, n}, {l, m, p}, {l, n, p}, {m, n, l}, {l, m, n, p} B) {l}, {m}, {n}, {p}, {l, m}, {l, n}, {l, p}, {m, n}, {m, p}, {n, p}, {l, m, n}, {l, m, p}, {l, n, p}, {l, m, n, p} C) ∅, {l}, {m}, {n}, {p}, {l, m}, {l, n}, {l, p}, {m, n}, {m, p}, {n, p}, {l, m, n}, {l, m, p}, {l, n, p}, {l, m, n, p} D) ∅, {l}, {m}, {n}, {p}, {l, m}, {l, n}, {m, n}, {m, p}, {n, p}, {l, m, n}, {l, m, p}, {l, n, p}, 135) A committee is to be formed. Possible candidates for the committee are Anne, Daniel, Raul, Sarah, and Teresa. Denoting these five people by a, d, r, s, t, list all possible committees of three people (ie list all possible subsets of size three). 135) _____ A) {a, d, r}, {a, d, s}, {a, d, t}, {a, r, s}, {a, r, t}, {a, s, t}, {d, r, t}, {d, s, t}, {r, s, t} B) {a, d, r}, {a, d, s}, {a, d, t}, {a, r, s}, {a, r, t}, {a, s, t}, {d, r, s}, {d, r, t}, {d, s, t}, {r, s, t}, C) {a, d, r}, {a, d, s}, {a, d, t}, {a, r, s}, {a, r, t}, {a, s, t}, {d, r, s}, {d, r, t}, {d, s, t}, {r, s, t} D) {a, d, r}, {a, d, s}, {a, d, t}, {a, r, s}, {d, r, s}, {d, r, t}, {d, s, t}, {r, s, t} 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}. 136) A ∪ C 136) _____ A) {q, s, u, v, w, x, y, z} B) {w, y} C) {q, s, u, v, w, y, z} D) {q, s, u, w, y, v, w, x, y, z} 137) B ∩ C 137) _____ A) {q, s, v, w, x, y, z} B) {y, z} C) {y} D) {w, y, z} 138) A ∩ B’ A) {t, v, x} C) {u, w} 138) _____ B) {q, s, t, u, v, w, x, y} D) {r, s, t, u, v, w, x, z} 139) (A ∪ B)’ 139) _____ A) {r, t, v, x} B) {s, u, w} C) {r, s, t, u, v, w, x, z} D) {t, v, x} 140) (A ∩ B)’ 140) _____ A) {t, v, x} B) {s, u, w} C) {q, s, t, u, v, w, x, y} D) {r, t, u, v, w, x, z} 141) A’ ∪ B 141) _____ A) {r, s, t, u, v, w, x, z} B) {q, r, s, t, v, x, y, z} C) {q, s, t, u, v, w, x, y} D) {s, u, w} 142) C’ ∪ A’ 142) _____ A) {w, y} B) {q, s, u, v, w, x, y, z} C) {s, t} D) {q, r, s, t, u, v, x, z} 143) C’ ∩ A’ 143) _____ A) {q, r, s, t, u, v, x, z} B) {w, y} C) {q, s, u, v, w, x, y, z} D) {r, t} 144) C – A A) {w, y} 144) _____ B) {q, s, u} C) {q, s, u, v, x, z} D) {v, x, z} 145) A’ – C A) {v, x, z} 145) _____ B) {q, s, u} C) {q, s, u, v, x, z} D) {r, t} 146) A ∪ (B ∩ C) 146) _____ A) {q, w, y} B) {q, y, z} C) {q, r, w, y, z} D) {q, s, u, w, y, z} 147) A ∩ (B ∪ C) 147) _____ A) {q, s, w, y} B) {q, r, w, y, z} C) {q, y, z} 148) (A’ ∪ C) ∩ B’ 148) _____ A) {r, t, u, v, w, s, y, z} B) {y, z} C) {r, t, v, w, x} D) {v, x} 149) (B’ ∩ C)’ ∪ A 149) _____ D) {q, s, u, w, y, z} A) {q, s, u, v, w, x, y} C) {q, r, s, t, u, w, y, z} B) {q, s, u, y} D) {q, r, s, t, u, v, w, x, y} 150) (A ∪ B’)’ ∩ C’ 150) _____ A) ∅ B) {q, r, s, t, u, z}C) {v, w, x, y} D) {q, r, s, t, u} 151) B ∩ (A – C) 151) _____ A) {q, s} B) {q, s, u, y} C) {q, s, u, y, z} D) {q, r, s, t, u, v, w, x, y} 152) (A ∩ B’) ∪ (B ∩ A’) A) {q, s, u, w, y, z} 152) _____ B) {u, w, y, z} C) {u, w, z} D) {q, s, y} Let U = {all soda pops}, A = {all diet soda pops}, B = {all cola soda pops}, Describe the set in words. 153) A ∩ B 153) _____ A) All soda pops B) All diet and all cola soda pops C) All diet cola soda pops D) All diet or all cola soda pops 154) A’ ∩ C 154) _____ A) All non-diet soda pops and all soda pops in cans B) All diet soda pops in cans C) All diet soda pops and all soda pops in cans D) All non-diet soda pops in cans 155) A ∩ B ∩ D 155) _____ A) All diet, caffeine-free cola pops in cans B) All soda pops not in cans C) All diet, caffeine-free cola soda pops D) All diet and all cola and all caffeine-free soda pops 156) (A ∪ B) ∪ D 156) _____ A) All diet, caffeine-free cola soda pops B) All soda pops not in cans C) All soda pops D) All diet or all cola or all caffeine-free soda pops 157) (A ∩ B) ∩ C’ 157) _____ A) All cola soda pops not in cans B) All non-diet, non-cola soda pops not in cans C) All diet cola soda pops not in cans D) All diet and all cola soda pops not in cans 158) (A ∪ D) ∩ C’ 158) _____ A) All diet, caffeine-free soda pops not in cans B) All non-cola soda pops not in cans C) All non-diet, non-caffeine-free soda pops not in cans D) All diet soda pops not in cans or all caffeine-free soda pops not in cans 159) (A’ ∩ B’) ∪ C 159) _____ A) All non-diet non-cola soda pops in cans B) All non-diet non-cola soda pops and all soda pops not in cans and C) All non-diet non-cola soda pops or all soda pops in cans D) All non-diet soda pops and all non-cola soda pops in cans 160) (A – D) ∩ B 160) _____ A) All diet soda pops that contain caffeine and all cola soda pops B) All non-diet, caffeine-free cola soda pops C) All diet cola soda pops that contain caffeine D) All diet caffeine-free cola soda pops 161) (B ∩ C’) ∪ (C ∩ B’ ) 161) _____ A) All cola soda pops in cans and all non-cola soda pops not in cans B) All cola soda pops and all soda pops in cans C) All cola soda pops not in cans or all non-cola soda pops in cans D) All non-cola soda pops not in cans The lists below show five agricultural crops in Alabama, Arkansas, and Louisiana. Alabama soybeans (s) peanuts (p) corn (c) hay (h) wheat (w) Arkansas soybeans (s) rice (r) cotton (t) hay (h) wheat (w) Louisiana soybeans (s) sugarcane (n) rice (r) corn (c) cotton (t) Let U be the smallest possible universal set that includes all of the crops listed, and let A, K and L be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find each of the following sets. 162) A ∩ K 162) _____ A) {c, p, r, t} B) {c, h, s, t, w} C) {c, h, p, r, s, t, w} D) {h, s, w} 163) L ∩ K A) {c, h, n, w} C) {r, s, t} 163) _____ B) {c, n, r, s, t} D) {c, h, n, r, s, t, w} 164) K’ ∩ L 164) _____ A) {c, n} B) {c, n, p} C) {h, w} D) {r, s, t} 165) L’ ∩ A A) {n, r, t} 165) _____ B) {h, n, t, w} 166) A’ ∩ K’ A) {c, p, r, t} 166) _____ B) ∅ C) {c, n, p, r, t} D) {n} C) {c, s} D) {h, p, w} 167) A ∩ K ∩ L 167) _____ A) {s} B) {c, h, n, p, r, s, t, w} C) {n, p, s} D) {n, p} 168) A ∪ L 168) _____ A) {c, s} B) {c, n, p} C) {c, h, n, p, r, s, t, w} D) {h, n, p, r, t, w} 169) K ∪ L 169) _____ A) {n, r, t} B) {r, s, t} C) {c, h, n, r, s, t, w} D) {c, h, n, w} 170) A’ ∪ L 170) _____ A) {h, n, p, r, t, w} B) {n, r, t} 171) L’ ∪ K’ A) {r, s, t} C) {c, n, r, s, t} D) {h, p, w} 171) _____ B) {c, h, n, p, w} C) {c, h, p, s, w} D) {p} Let A and B be sets with cardinal numbers, n(A) = a and n(B) = b, respectively. Decide whether the statement is true or false. 172) n(A ∪ B) = n(A) – n(B) 172) _____ A) True B) False 173) n(A – B) = n(B – A) 173) _____ A) True B) False 174) If B ⊆ A, n(B) = n(A – B). A) True B) False 174) _____ 175) If B ⊆ A, n(B) = n(A) – n(A – B). A) True B) False 175) _____ 176) n(A ∩ B) = n(B ∩ A) 176) _____ A) True B) False 177) n(A ∪ B) = n(A) + n(B) – n(A ∩ B) A) True B) False 178) n(A ∩ B) = n(A) – n(B) A) True B) False 177) _____ 178) _____ 179) n(A ∪ B) + n(A ∩ B) = n(A) + n(B) A) True B) False 179) _____ Tell whether the statement is true or false. 180) {3, 9, 15} = {0, 3, 9, 15} 180) _____ A) True B) False 181) {52, 53, 52, 53} = {52, 53} A) True B) False 181) _____ 182) {6, 16, 24, 8, 33} = {33, 16, 8, 42, 6} A) True B) False 183) (2, 7) = (7, 2) A) True B) False 182) _____ 183) _____ 184) (5 – 8, 4 – 15) = (-3, -11) A) True B) False 184) _____ 185) (16 + 10, 19 + 10) = (16, 19) 185) _____ A) True B) False 186) {(3, 1), (0, 6), (-4, -2)} = {(-4, -2), (3, 1), (6, 0)} A) True B) False 186) _____ Find the Cartesian product. 187) A = {8, 4, 11} B = {14, 15} Find A × B. 187) _____ A) {(8, 14), (4, 11), (11, 14)} B) {(14, 8), (14, 4), (14, 11), (15, 8), (15, 4), (15, 11)} C) {(8, 14), (8, 15), (4, 14), (4, 15), (11, 14), (11, 15)} D) {(8, 14), (4, 15)} 188) A = {i, a} B = {t, d, m} Find A × B. 188) _____ A) {(i, t), (t, a), (i, d), (d, a), (i, m), (m, a)} B) {(t, i), (t, a), (d, i), (d, a), (m, i), (m, a)} C) {(i, t), (a, t), (i, d), (a, d)} D) {(i, t), (i, d), (i, m), (a, t), (a, d), (a, m)} 189) A = {0} B = {19, 29, 39} Find B × A. 189) _____ A) {(19, 0), (29, 0), (39, 0)} B) {0, 0, 0} C) {0} D) {(0, 19), (0, 29), (0, 39)} 190) A = {4, 3, 6, 7} B = {0, 1} Find B × A. 190) _____ A) {(4, 0), (4, 1), (3, 0), (3, 1)} B) {0, 1, 4, 3, 6, 7} C) {(4, 0), (3, 0), (6, 0), (7, 0), (4, 1), (3, 1), (6, 1), (7, 1)} D) {(0, 4), (0, 3), (0, 6), (0, 7), (1, 4), (1, 3), (1, 6), (1, 7)} Find the indicated cardinal number. 191) Find n(A × B) given that A = {2} and B = {1, 3}. A) 1 B) 4 C) 2 D) 3 192) Find n(A × C) given that A = {2} and C = {4, 5, 6}. A) 2 B) 1 C) 3 D) 4 191) _____ 192) _____ 193) Find n(D × B) given that B = {1, 3} and D = {7, 8, 9, 10}. A) 7 B) 16 C) 12 D) 8 193) _____ 194) Find n(C × D) given that C = {4, 5, 6} and D = {7, 8, 9, 10}. A) 27 B) 12 C) 81 D) 7 194) _____ 195) Find n(E), given that n(C × E) = 18 and C = {4, 5, 6}. 195) _____ A) 6 B) 54 C) 3 D) 9 196) Find n(F), given that n(B × F) = 18 and B = {1, 3}. A) 54 B) 6 C) 36 D) 9 196) _____ 197) Find n(G), given that n(D × G) = 20 and D = {7, 8, 9, 10}. A) 4 B) 9 C) 24 D) 5 197) _____ 198) Find n(A × B) given that n(A) = 40 and n(B) = 7. A) 47 B) 280 C) 33 D) 54 198) _____ 199) Find n(B) given that n(A × B) = 30 and n(A) = 3 . A) 27 B) 3 C) 10 D) 33 199) _____ 200) Find n(A) given that n(A × B) = 22 and n(B) = 2. A) 24 B) 20 C) 11 D) 2 200) _____ For the given sets, construct a Venn diagram and place the elements in the proper region. 201) Let U = {c, d, g, h, k, u, q} A = {d, h, g, q} B = {c, d, h, u} 201) _____ A) B) C) D) 202) Let U = {1, 2, 3, 4, 5, 6, 7, 8} A = {3, 6, 8} B = {4, 6} C = {1, 6, 7, 8} 202) _____ A) B) C) D) 203) Let U = {c, e, f, j, q, m, w} A = {e, f, j, m} B = {c, e, f, w} 203) _____ A) B) C) D) 204) U = {2, 4, 6, 8, 10, 12} A = {2, 6, 10} B = {2, 4, 8} C = {2, 8, 10, 12} 204) _____ A) B) C) D) 205) U = {a, b, c, d, e, f, g, h, i,j , k, l, m, n, o, p} A = {a, e, i, o} B = {b, c, d, f, g, h, j, k, l, m} C = {a, b, c, d, e, f, g} 205) _____ A) B) C) D) Shade the regions representing the set. 206) A’ ∩ B’ 206) _____ A) B) C) D) 207) A’ ∪ B’ 207) _____ A) B) C) D) 208) (A ∪ B) ∩ (A ∩ B)’ 208) _____ A) B) C) D) 209) (A ∩ B) ∪ (A ∪ B)’ 209) _____ A) B) C) D) 210) (A ∩ B ∩ C’)’ 210) _____ A) B) C) D) 211) (A ∪ B ∪ C’)’ 211) _____ A) B) C) D) 212) C’ ∩ (A ∪ B) 212) _____ A) B) C) D) 213) (A’ ∪ B) ∩ C 213) _____ A) B) C) D) 214) A ∪ (B ∩ C’) 214) _____ A) B) C) D) 215) B ∪ (A ∩ C’) 215) _____ A) B) C) D) Write a description of the shaded region using the symbols A, B, C, ∪, ∩, -, and as needed. 216) 216) _____ A) B ∩ B) B – C) A – B D) A ∩ 217) 217) _____ A) A – BB) C) A ∪ B D) ∩ 218) 218) _____ A) B – AB) ∪B C) ∩B D) 219) 219) _____ A) A ∩ B B) (A ∩ B)’ C) (A ∪ B)’ 220) 220) _____ A) (A ∩ B) ∪ (A ∩ B)’ C) (A ∩ B) ∪ (A ∪ B)’ 221) B) (A – B) ∪ (B -A) D) A’ ∩ B’ D) A’ ∩ B’ 221) _____ A) (A ∪ B) ∩ C’ B) (A ∪ B) ∪ C’ C) (A ∩ B) ∩ C’ D) (A ∪ B) ∩ C 222) 222) _____ A) A’ ∩ C B) (A ∪ B’) ∩ C C) (A’ ∩ B) ∪ C D) (A’ ∪ B) ∩ C 223) 223) _____ A) (A ∩ B) ∪ B) ( C) A ∪ B ∩ D) (A ∪ B) ∪ 224) 224) _____ A) B – (A ∩ C) B) (B – A) ∪ C C) B ∩ D) ∩ 225) 225) _____ A) ∩A∪C B) C ∩ ∪A C) A ∪ C – B D) A ∪ C ∩B Decide whether the given statement is always true or not always true. 226) A ∩ = ∅ 226) _____ A) Always true B) Not always true 227) (A ∪ B) ⊆ A 227) _____ A) Always true B) Not always true 228) (A ∩ B) ⊆ B 228) _____ A) Not always true B) Always true 229) = ∪ 229) _____ A) Always true B) Not always true 230) = ∪ 230) _____ A) Always true B) Not always true 231) If A ⊆ B, then A ∪ B = A 231) _____ A) Not always true B) Always true 232) If B ⊆ A, then A ∩ B = A 232) _____ A) Always true B) Not always true 233) A = A 233) _____ A) Not always true B) Always true 234) A ∪ (B ∩ C)’ = A ∪ (B’ ∪ C’) 234) _____ A) Always true B) Not always true 235) A ∩ (B ∪ C) = (A ∩ B) ∪ C 235) _____ A) Always true B) Not always true Describe the conditions under which the statement is true. 236) A ∩ B = A 236) _____ A) A ⊆ B B) B = ∅ C) Always true D) B ⊆ A 237) A ∪ ∅ = U 237) _____ A) A = U B) A = ∅C) Always true D) A ≠ ∅ 238) A ∪ B = B A) A ⊆ B 238) _____ B) Always true C) A = ∅ 239) A ∩ A’ = A 239) _____ A) Always true B) A = ∅C) A ≠ ∅ D) B ⊆ A D) A = U 240) A ∩ B’ = A 240) _____ A) Always true B) B ⊆ A C) B = ∅ D) A ∩ B = ∅ 241) A ∪ B = A 241) _____ A) Always true B) A ⊆ B C) B ⊆ A Find the cardinal number of the set. D) B = ∅ 242) The numbers in the Venn Diagram below represent cardinalities. Find n(A ∪ B). 242) _____ A) 48 B) 24 C) 4 D) 52 243) The numbers in the Venn Diagram below represent cardinalities. Find n(A ∩ B’). 243) _____ A) 28 B) 24 C) 20 D) 4 244) The numbers in the Venn Diagram below represent cardinalities. Find n(A’ ∩ B’ ∩ C) 244) _____ A) 27 D) 13 B) 14 C) 21 245) The numbers in the Venn Diagram below represent cardinalities. Find n(A ∩ B’ ∩ C) 245) _____ A) 11 D) 15 B) 6 C) 7 246) The numbers in the Venn Diagram below represent cardinalities. Find n(B ∪ C) 246) _____ A) 60 C) 42 B) 49 D) 14 247) Given: n(U) = 60 n(A) = 30 n(B) = 16 n(A ∩ B) = 6 Find n(A ∪ B)’. 247) _____ A) 20 B) 40 C) 14 248) Given: n(U) = 213 n(A) = 72 n(B) = 92 n(A ∩ B) n(A ∩ C) n(A ∩ B ∩ C) n(A’ ∩ B ∩ C’) n(A’ ∩ B’ ∩ C’) Find n(C). D) 46 = 31 = 34 = 16 = 45 = 54 248) _____ A) 26 B) 76 C) 44 249) Given: n(A) = 60 n(B) = 68 n(C) = 62 n(A ∩ B) n(A ∩ C) n(B ∩ C)= 8 D) 42 = 12 = 14 n(A ∩ B ∩ C) n(A’ ∩ B’ ∩ C’) Find n(U) =6 = 121 249) _____ A) 293 B) 283 C) 222 D) 162 250) Given: n(A ∪ B ∪ C) n(A ∩ B ∩ C) = 22 n(A ∩ B) = 46 n(A ∩ C) = 43 n(B ∩ C)= 41 n(A) = 111 n(B) = 82 n(C) = 80 Find n(A’ ∩ B ∩ C) = 165 250) _____ A) 21 B) 20 C) 18 D) 19 Find the cardinal number of the indicated set. Use the cardinal number formula. 251) If n(A) = 4, n(B) = 9 and n(A ∩ B) = 2, what is n(A ∪ B)? 251) _____ A) 12 B) 11 C) 10 D) 13 252) If n(A) = 40, n(B) = 117 and n(A ∪ B) = 137, what is n(A ∩ B)? 252) _____ A) 60 B) 22 C) 20 D) 10 253) If n(B) = 60, n(A ∩ B) = 11, and n(A ∪ B) = 105, find n(A). A) 58 B) 45 C) 56 D) 54 253) _____ 254) If n(A) = 25, n(A ∪ B) = 73, and n(A ∩ B) = 21, find n(B). A) 70 B) 68 C) 48 D) 69 254) _____ Draw an appropriate Venn diagram and use the given information to fill in the number of elements in each region. 255) n(U) = 52, n(A) = 28, n(A ∩ B) = 4, n( ) = 28 255) _____ A) B) C) D) 256) n(A) = 14, n(B) = 21, n(A ∪ B) = 25, n( ) = 9 256) _____ A) B) C) D) 257) n( A) ) = 26, n(B) = 32, n(A ∩ B) = 11, n( B) ) = 35 257) _____ C) D) 258) n(A) = 30, n(B) = 28, n(C) = 35, n(A ∩ B) = 12, n(A ∩ C) = 15, n(B ∩ C) = 14, n(U) = 67 A) 258) _____ B) C) D) 259) n(A) = 48, n( ) = 60, n(C) = 51, n(A ∩ B) = 20, n(B ∩ C) = 19, n(A ∩ C) = 18, _____ A) 259) B) C) D) 260) n(A) = 35, n(A ∩ ) = 24, n(A ∩ C) = 15, n(B ∩ C) = 14, n( 260) _____ A) B) C) D) ∩ ∩ ) = 10, Solve the problem. 261) Mrs. Bollo’s second grade class of thirty students conducted a pet ownership survey. Results of the survey indicate that 8 students own a cat, 15 students own a dog, and 5 students own both a cat and a dog. How many of the students surveyed own no cats? 261) _____ A) 15 B) 10 C) 27 D) 22 262) Monticello residents were surveyed concerning their preferences for candidates Moore and Allen 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 Moore or Allen? 262) _____ A) 500 B) 400 C) 300 D) 100 263) A local television station sent out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 900 responses with the following results: 270 were interested in an interview show and a documentary, but not reruns. 36 were interested in an interview show and reruns but not a documentary. 126 were interested in reruns but not an interview show. 216 were interested in an interview show but not a documentary. 90 were interested in a documentary and reruns. 54 were interested in an interview show and reruns. 72 were interested in none of the three. How many are interested in exactly one kind of show? 263) _____ A) 412 B) 442 C) 422 D) 432 264) A survey of 260 families showed that 99 had a dog; 76 had a cat; 34 had a dog and a cat; 98 had neither a cat nor a dog nor a parakeet; 8 had a cat, a dog, and a parakeet. How many had a parakeet only? A) 26 B) 21 C) 36 264) _____ D) 31 265) A survey of a group of 113 tourists was taken in St. Louis. The survey showed the following: 63 of the tourists plan to visit Gateway Arch; 49 plan to visit the zoo; 10 plan to visit the Art Museum and the zoo, but not the gateway Arch; 12 plan to visit the Art Museum and the Gateway Arch, but not the zoo; 17 plan to visit the Gateway Arch and the zoo, but not the Art Museum; 9 plan to visit the Art Museum, the zoo, and the Gateway Arch; 15 plan to visit none of the three places. How many plan to visit the Art Museum only? 265) _____ A) 98 B) 36 C) 49 D) 12 266) In a survey of 280 people, a travel company asked people about places they plan to visit in the next 5 years. The results were as follows: 48 plan to visit Europe 58 plan to visit Latin America 34 plan to visit Asia 14 plan to visit Europe and Latin America 12 plan to visit Latin America and Asia 11 plan to visit Europe and Asia 4 plan to visit all three How many people plan to visit exactly two of these places? A) 29 B) 18 C) 37 266) _____ D) 25 267) A survey of 125 college students was done to find out what elective courses they were taking. Let A = the set of those taking art, B = the set of those taking basketweaving, and C = the set of those taking canoeing. The study revealed the following information. n(A) = 45 n(A ∩ B) = 12 n(B) = 55 n(A ∩ C) = 15 n(C) = 40 n(B ∩ C) = 23 n(A ∩ B ∩ C) = 2 How many students were not taking any of these electives? A) 33 B) 43 C) 10 D) 35 267) _____ 1) A 2) C 3) B 4) A 5) C 6) A 7) B 8) C 9) C 10) B 11) D 12) D 13) D 14) A 15) A 16) B 17) A 18) D 19) B 20) C 21) B 22) B 23) A 24) B 25) B 26) A 27) A 28) B 29) D 30) C 31) A 32) B 33) A 34) B 35) C 36) C 37) D 38) B 39) B 40) A 41) B 42) B 43) B 44) B 45) A 46) A 47) A 48) A 49) B 50) A 51) A 52) B 53) B 54) A 55) B 56) B 57) A 58) B 59) A 60) B 61) B 62) A 63) B 64) A 65) B 66) A 67) B 68) A 69) B 70) A 71) B 72) B 73) B 74) B 75) A 76) A 77) B 78) A 79) B 80) B 81) B 82) B 83) C 84) B 85) C 86) A 87) A 88) A 89) B 90) B 91) A 92) B 93) B 94) B 95) A 96) B 97) A 98) B 99) D 100) C 101) C 102) D 103) D 104) D 105) B 106) A 107) B 108) D 109) A 110) D 111) A 112) A 113) C 114) B 115) B 116) C 117) D 118) D 119) C 120) C 121) A 122) B 123) B 124) A 125) A 126) A 127) C 128) A 129) A 130) D 131) A 132) D 133) A 134) C 135) C 136) A 137) B 138) C 139) A 140) D 141) B 142) D 143) D 144) D 145) D 146) D 147) A 148) C 149) C 150) A 151) A 152) C 153) C 154) D 155) C 156) D 157) C 158) D 159) C 160) C 161) C 162) D 163) C 164) A 165) D 166) D 167) A 168) C 169) C 170) C 171) B 172) B 173) B 174) B 175) A 176) A 177) A 178) B 179) A 180) B 181) A 182) B 183) B 184) A 185) B 186) B 187) C 188) D 189) A 190) D 191) C 192) C 193) D 194) B 195) A 196) D 197) D 198) B 199) C 200) C 201) D 202) C 203) D 204) A 205) A 206) B 207) C 208) D 209) C 210) B 211) B 212) A 213) B 214) A 215) C 216) A 217) D 218) B 219) B 220) C 221) A 222) D 223) D 224) D 225) B 226) A 227) B 228) B 229) A 230) B 231) A 232) B 233) B 234) A 235) B 236) A 237) A 238) A 239) B 240) D 241) C 242) A 243) B 244) B 245) C 246) B 247) A 248) B 249) B 250) D 251) B 252) C 253) C 254) D 255) B 256) D 257) A 258) D 259) B 260) C 261) D 262) A 263) D 264) B 265) D 266) D 267) A