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mathematics
contemporary mathematics
Contemporary Mathematics 1st Edition OpenStax - Solutions
Find \(n\left(A \cap \mathrm{Rh}^{+}\right)\).A blood drive at City Honors High School recently collected blood from 140 students, staff, and faculty. Use the results depicted in the Venn diagram below to answer the following exercise. Donors = 140 A 8 2 3 50 4 11 B 52 Rh+ 10
Find \(n\left(A \cup \mathrm{Rh}^{+}\right)\).A blood drive at City Honors High School recently collected blood from 140 students, staff, and faculty. Use the results depicted in the Venn diagram below to answer the following exercise. Donors = 140 A 8 2 3 50 4 11 B 52 Rh+ 10
Find \(n\left(A \cap B \cap \mathrm{Rh}^{-}\right)\).A blood drive at City Honors High School recently collected blood from 140 students, staff, and faculty. Use the results depicted in the Venn diagram below to answer the following exercise. Donors = 140 A 8 2 3 50 4 11 B 52 Rh+ 10
The number of elements in the universal set, \(U\), is \(n(U)=48\). Sets \(A, B\), and \(C\) are subsets of \(U\) : \(n(A)=23, n(B)=25\), and \(n(C)=17\). Also, \(n(A \cap B)=15, n(B \cap C)=12, n(C \cap A)=11\), and \(n(A \cap B \cap C)=8\).Create a three circle Venn diagram to represent the
The number of elements in the universal set, \(U\), is \(n(U)=88\). Sets \(A, B\), and \(C\) are subsets of \(U\) : \(n(A)=31, n(B)=46: n(C)=33\). Also, \(n(A \cap B)=24, n(B \cap C)=24, n(C \cap A)=26\), and \(n(A \cap B \cap C)=22\).Create a three circle Venn diagram to represent the relationship
The number of elements in the universal set, \(U\), is \(n(U)=52\). Sets \(A, B\), and \(C\) are subsets of \(U: n(A)=23\), \(n(B)=27\), and \(n(C)=29\). Also, \(n(A \cap B)=22, n(B \cap C)=21, n(C \cap A)=19\), and \(n(A \cap B \cap C)=18\).Create a three circle Venn diagram to represent the
The number of elements in the universal set, \(U\), is \(n(U)=144\). Sets \(A, B\), and \(C\) are subsets of \(U: n(A)=36\), \(n(B)=64\), and \(n(C)=81\). Also, \(n(A \cap B)=26, n(B \cap C)=61, n(C \cap A)=29\), and \(n(A \cap B \cap C)=25\).Create a three circle Venn diagram to represent the
The universal set, \(U\), has a cardinality of 36 .\(n(A)=12, n(B)=12, n(C)=15, n(A\) and \(B)=3, n(B\) and \(C)=4, n(C\) and \(A)=5, n(C\) and \(A)=5\), and \(n(A\) and \(B\) and \(C)=1\).Create a three circle Venn diagram to represent the relationship between the described sets.
The universal set, \(U\), has a cardinality of \(63 . n(A)=29\),\(n(B)=31, n(C)=41, n(A\) and \(B)=12, n(B\) and \(C)=16, n(C\) and \(A)=18\), and \(n(A\) and \(B\) and \(C)=5\).Create a three circle Venn diagram to represent the relationship between the described sets.
The universal set, \(U\), has a cardinality of 72 .\(n(A)=32, n(B)=32, n(C)=44, n(A\) and \(B)=18, n(B\) and \(C)=22, n(C\) and \(A)=26\), and \(n(A\) and \(B\) and \(C)=14\).Create a three circle Venn diagram to represent the relationship between the described sets.
The universal set, \(U\), has a cardinality of 81 .\(n(A)=54, n(B)=41, n(C)=52, n(A\) and \(B)=32, n(B\) and \(C)=28, n(C\) and \(A)=30\), and \(n(A\) and \(B\) and \(C)=21\).Create a three circle Venn diagram to represent the relationship between the described sets.
The anime drawing club at Pratt Institute conducted a survey of its 42 members and found that 23 of them sketched with pastels, 28 used charcoal, and 17 used colored pencils. Of these, 10 club members used all three mediums, 18 used charcoal and pastels, 11 used colored pencils and charcoal, and 12
A new SUV is selling with three optional packages: a sport package, a tow package, and an entertainment package. A dealership gathered the following data for all 31 of these vehicles sold during the month of July. A total of 18 SUVs included the entertainment package, 11 included the tow package,
Find \((A \cup B) \cap C\).Perform the set operations as indicated on the following sets: \(U=\{\) red, orange, yellow, green, blue, indigo, violet \(\}, A=\{\) red, yellow, blue \(\}, B=\{\) orange, green, violet \(\}\), and \(C=\{\) red, green, indigo \(\}\).
Find \((A \cap C) \cup B\).Perform the set operations as indicated on the following sets: \(U=\{\) red, orange, yellow, green, blue, indigo, violet \(\}, A=\{\) red, yellow, blue \(\}, B=\{\) orange, green, violet \(\}\), and \(C=\{\) red, green, indigo \(\}\).
Find \(U \cap(B \cup C)\).Perform the set operations as indicated on the following sets: \(U=\{\) red, orange, yellow, green, blue, indigo, violet \(\}, A=\{\) red, yellow, blue \(\}, B=\{\) orange, green, violet \(\}\), and \(C=\{\) red, green, indigo \(\}\).
Find \((B \cap A) \cap U\).Perform the set operations as indicated on the following sets: \(U=\{\) red, orange, yellow, green, blue, indigo, violet \(\}, A=\{\) red, yellow, blue \(\}, B=\{\) orange, green, violet \(\}\), and \(C=\{\) red, green, indigo \(\}\).
Find \(A \cap(B \cap C)^{\prime}\).Perform the set operations as indicated on the following sets: \(U=\{\) red, orange, yellow, green, blue, indigo, violet \(\}, A=\{\) red, yellow, blue \(\}, B=\{\) orange, green, violet \(\}\), and \(C=\{\) red, green, indigo \(\}\).
Find \(A^{\prime} \cap(B \cup C)\).Perform the set operations as indicated on the following sets: \(U=\{\) red, orange, yellow, green, blue, indigo, violet \(\}, A=\{\) red, yellow, blue \(\}, B=\{\) orange, green, violet \(\}\), and \(C=\{\) red, green, indigo \(\}\).
Find \(A\) and \(B\) and \(C^{\prime}\).Perform the set operations as indicated on the following sets: \(U=\{20,21,22, \ldots, 29\}, A=\{21,24,27\}, B=\{20,22,24,28\}\), and \(C=\{21,23,25,27\}\).
Find \(A^{\prime}\) or \(B\) or \(C\).Perform the set operations as indicated on the following sets: \(U=\{20,21,22, \ldots, 29\}, A=\{21,24,27\}, B=\{20,22,24,28\}\), and \(C=\{21,23,25,27\}\).
Find \((A\) or \(B)\) and \(C^{\prime}\).Perform the set operations as indicated on the following sets: \(U=\{20,21,22, \ldots, 29\}, A=\{21,24,27\}, B=\{20,22,24,28\}\), and \(C=\{21,23,25,27\}\).
Find \((A\) or \(B)\) or \(C^{\prime}\).Perform the set operations as indicated on the following sets: \(U=\{20,21,22, \ldots, 29\}, A=\{21,24,27\}, B=\{20,22,24,28\}\), and \(C=\{21,23,25,27\}\).
Find \((A\) and \(C)\) and \(B^{\prime}\).Perform the set operations as indicated on the following sets: \(U=\{20,21,22, \ldots, 29\}, A=\{21,24,27\}, B=\{20,22,24,28\}\), and \(C=\{21,23,25,27\}\).
Find \((A \text { or } B)^{\prime}\) and \(C\).Perform the set operations as indicated on the following sets: \(U=\{20,21,22, \ldots, 29\}, A=\{21,24,27\}, B=\{20,22,24,28\}\), and \(C=\{21,23,25,27\}\).
Commutative property for the union of two sets: \(A \cup B=B \cup A\).Use Venn diagrams to prove the following properties of sets:
Commutative property for the intersection of two sets: \(A \cap B=B \cap A\).Use Venn diagrams to prove the following properties of sets
Associative property for the intersection of three sets: \((A \cap B) \cap C=A \cap(B \cap C)\).Use Venn diagrams to prove the following properties of sets
Associative property for the union of three sets: \(A \cup(B \cup C)=(A \cup B) \cup C\).Use Venn diagrams to prove the following properties of sets
Distributive property for set intersection over set union: \(A \cap(B \cup C)=(A \cap B) \cup(A \cap C)\).Use Venn diagrams to prove the following properties of sets
Distributive property for set union over set intersection: \(A \cup(B \cap C)=(A \cup B) \cap(A \cup C)\).Use Venn diagrams to prove the following properties of sets
Interpret each Venn diagram and describe the relationship between the sets, symbolically and in words. U = Sports T = Team Sports
Interpret each Venn diagram and describe the relationship between the sets, symbolically and in words. U = Fruit A = Apples
Interpret each Venn diagram and describe the relationship between the sets, symbolically and in words. U = Writing Utensils P = Pencils
Interpret each Venn diagram and describe the relationship between the sets, symbolically and in words. U = Games B Board Games
Interpret each Venn diagram and describe the relationship between the sets, symbolically and in words. U Writing Utensils C = Crayons P = Pencils
Interpret each Venn diagram and describe the relationship between the sets, symbolically and in words. U = Fruit A = Apples P = Pears
Interpret each Venn diagram and describe the relationship between the sets, symbolically and in words. U = Games A = Card Games B = Video Games
Interpret each Venn diagram and describe the relationship between the sets, symbolically and in words. U = Investments A = Stocks B = Bonds
All birds have wings.Create a Venn diagram to represent the relationships between the sets.
All cats are animals.Create a Venn diagram to represent the relationships between the sets.
All almonds are nuts, and all pecans are nuts, but no almonds are pecans.Create a Venn diagram to represent the relationships between the sets.
All rectangles are quadrilaterals, and all trapezoids are quadrilaterals, but no rectangles are trapezoids.Create a Venn diagram to represent the relationships between the sets.
Lizards \(\subset\) Reptiles.Create a Venn diagram to represent the relationships between the sets.
Ladybugs \(\subset\) Insects.Create a Venn diagram to represent the relationships between the sets.
Ladybugs \(\subset\) Insects and Ants \(\subset\) Insects, but no Ants are Ladybugs.Create a Venn diagram to represent the relationships between the sets.
Lizards \(\subset\) Reptiles and Snakes \(\subset\) Reptiles, but no Lizards are Snakes.Create a Venn diagram to represent the relationships between the sets.
\(A\) and \(B\) are disjoint subsets of \(U\).Create a Venn diagram to represent the relationships between the sets.
\(C\) and \(D\) are disjoint subsets of \(U\).Create a Venn diagram to represent the relationships between the sets.
\(T\) is a subset of \(U\).Create a Venn diagram to represent the relationships between the sets.
\(S\) is a subset of \(U\).Create a Venn diagram to represent the relationships between the sets.
\(J=\) Jazz, \(M=\) Music, and \(J \subset M\).Create a Venn diagram to represent the relationships between the sets.
\(R=\) Reggae, \(M=\) Music, and \(R \subset M\).Create a Venn diagram to represent the relationships between the sets.
\(J=\) Jazz, \(R=\) Reggae, and \(M=\) Music are sets with the following relationships: \(J \subset M, R \subset M\), and \(R\) is disjoint from \(J\).Create a Venn diagram to represent the relationships between the sets.
\(J=\) Jazz, \(B=\) Bebop, and \(M=\) Music are sets with the following relationships: \(J \subset M\) and \(B \subset J\).Create a Venn diagram to represent the relationships between the sets.
\(A=\{6,7,8\}\)The universal set is the set of single digit numbers, \(U=\{0,1,2,3,4,5,6,7,8,9\}\). Find the complement of each subset of \(U\).
\(A=\{0,2,4,6,8\}\)The universal set is the set of single digit numbers, \(U=\{0,1,2,3,4,5,6,7,8,9\}\). Find the complement of each subset of \(U\).
\(A=\{\}\)The universal set is the set of single digit numbers, \(U=\{0,1,2,3,4,5,6,7,8,9\}\). Find the complement of each subset of \(U\).
\(A=\{0,1,4,6,8,9\}\)The universal set is the set of single digit numbers, \(U=\{0,1,2,3,4,5,6,7,8,9\}\). Find the complement of each subset of \(U\).
\(A=\{0,1,2,3,4,5,6,7,8,9\}\)The universal set is the set of single digit numbers, \(U=\{0,1,2,3,4,5,6,7,8,9\}\). Find the complement of each subset of \(U\).
\(A=\{0,1,3,4,5,6,7,9\}\)The universal set is the set of single digit numbers, \(U=\{0,1,2,3,4,5,6,7,8,9\}\). Find the complement of each subset of \(U\).
\(A=\{1,2,3,4,5,6,7,8,9\}\)The universal set is the set of single digit numbers, \(U=\{0,1,2,3,4,5,6,7,8,9\}\). Find the complement of each subset of \(U\).
\(A=\{0,3,6,9\}\)The universal set is the set of single digit numbers, \(U=\{0,1,2,3,4,5,6,7,8,9\}\). Find the complement of each subset of \(U\).
\(A=\{\) Happy, Bashful, Grumpy \(\}\)The universal set is \(U=\{\) Bashful, Doc, Dopey, Grumpy, Happy, Sleepy, Sneezy \(\}\). Find the complement of each subset of \(U\).
\(A=\{\) Sleepy, Sneezy \(\}\)The universal set is \(U=\{\) Bashful, Doc, Dopey, Grumpy, Happy, Sleepy, Sneezy \(\}\). Find the complement of each subset of \(U\).
\(A=\{\mathrm{Doc}\}\)The universal set is \(U=\{\) Bashful, Doc, Dopey, Grumpy, Happy, Sleepy, Sneezy \(\}\). Find the complement of each subset of \(U\).
\(A=\{\) Doc, Dopey \(\}\)The universal set is \(U=\{\) Bashful, Doc, Dopey, Grumpy, Happy, Sleepy, Sneezy \(\}\). Find the complement of each subset of \(U\).
\(A=\varnothing\)The universal set is \(U=\{\) Bashful, Doc, Dopey, Grumpy, Happy, Sleepy, Sneezy \(\}\). Find the complement of each subset of \(U\).
\(A=\{\) Doc, Grumpy, Happy, Sleepy, Bashful, Sneezy, Dopey \(\}\)The universal set is \(U=\{\) Bashful, Doc, Dopey, Grumpy, Happy, Sleepy, Sneezy \(\}\). Find the complement of each subset of \(U\).
\(A=\{1,2,3,4,5\}\)The universal set is \(U=\mathbb{N}=\{1,2,3, \ldots\}\). Find the complement of each subset of \(U\).
\(A=\{1,3,5, \ldots\}\)The universal set is \(U=\mathbb{N}=\{1,2,3, \ldots\}\). Find the complement of each subset of \(U\).
\(A=\{1\}\)The universal set is \(U=\mathbb{N}=\{1,2,3, \ldots\}\). Find the complement of each subset of \(U\).
\(A=\{4,5,6, \ldots\}\)The universal set is \(U=\mathbb{N}=\{1,2,3, \ldots\}\). Find the complement of each subset of \(U\).
Use the Venn diagram to determine the members of the complement of set \(A, A^{\prime}\). U= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} A= {2, 3, 4, 9}
Use the Venn diagram to determine the members of the complement of set \(A, A^{\prime}\). U {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} A = {1, 2, 4, 8}
Use the Venn diagram to determine the members of the complement of set \(A, A^{\prime}\). U = {1, i, s, t, e, n} A = {n, e, t}
Use the Venn diagram to determine the members of the complement of set \(A, A^{\prime}\). U= {1, i, s, t, e, n} A = {, i, n, e, s
\(B \cup C\)Determine the union or intersection of the sets as indicated. \(A=\{2,4,6,8,10,12\}, B=\{4,8,12,16,20\}, C=\{8,16,24,32,40\}\), and \(D=\{10,20,30,40,50\}\).
\(A \cap D\)Determine the union or intersection of the sets as indicated. \(A=\{2,4,6,8,10,12\}, B=\{4,8,12,16,20\}, C=\{8,16,24,32,40\}\), and \(D=\{10,20,30,40,50\}\).
\(D \cap C\)Determine the union or intersection of the sets as indicated. \(A=\{2,4,6,8,10,12\}, B=\{4,8,12,16,20\}, C=\{8,16,24,32,40\}\), and \(D=\{10,20,30,40,50\}\).
\(A \cup D\)Determine the union or intersection of the sets as indicated. \(A=\{2,4,6,8,10,12\}, B=\{4,8,12,16,20\}, C=\{8,16,24,32,40\}\), and \(D=\{10,20,30,40,50\}\).
\(A \cap(C \cup D)\)Determine the union or intersection of the sets as indicated. \(A=\{2,4,6,8,10,12\}, B=\{4,8,12,16,20\}, C=\{8,16,24,32,40\}\), and \(D=\{10,20,30,40,50\}\).
\(B \cup(A \cap D)\)Determine the union or intersection of the sets as indicated. \(A=\{2,4,6,8,10,12\}, B=\{4,8,12,16,20\}, C=\{8,16,24,32,40\}\), and \(D=\{10,20,30,40,50\}\).
\(D \cup(A \cap C)\)Determine the union or intersection of the sets as indicated. \(A=\{2,4,6,8,10,12\}, B=\{4,8,12,16,20\}, C=\{8,16,24,32,40\}\), and \(D=\{10,20,30,40,50\}\).
\(C \cap(A \cup D)\)Determine the union or intersection of the sets as indicated. \(A=\{2,4,6,8,10,12\}, B=\{4,8,12,16,20\}, C=\{8,16,24,32,40\}\), and \(D=\{10,20,30,40,50\}\).
\(B \cap(A \cap D)\)Determine the union or intersection of the sets as indicated. \(A=\{2,4,6,8,10,12\}, B=\{4,8,12,16,20\}, C=\{8,16,24,32,40\}\), and \(D=\{10,20,30,40,50\}\).
\(B \cap(A \cap C)\)Determine the union or intersection of the sets as indicated. \(A=\{2,4,6,8,10,12\}, B=\{4,8,12,16,20\}, C=\{8,16,24,32,40\}\), and \(D=\{10,20,30,40,50\}\).
\(B \cup(A \cup D)\)Determine the union or intersection of the sets as indicated. \(A=\{2,4,6,8,10,12\}, B=\{4,8,12,16,20\}, C=\{8,16,24,32,40\}\), and \(D=\{10,20,30,40,50\}\).
\(B \cup(A \cup C)\)Determine the union or intersection of the sets as indicated. \(A=\{2,4,6,8,10,12\}, B=\{4,8,12,16,20\}, C=\{8,16,24,32,40\}\), and \(D=\{10,20,30,40,50\}\).
Find the set consisting of elements in \(S\) and \(P\).Use the sets provided to apply the "AND" or "OR" operation as indicated to find the resulting set. \(U=\{a, b, c, \ldots, z\}, S=\{s, a, m, p, l, e\}, M=\{m, a, p\}, L=\{l, a, m, p\}, D=\{d, o, g\}\), and \(P=\{p, l, o, t\}\).
Find the set consisting of elements in \(M\) or \(D\).Use the sets provided to apply the "AND" or "OR" operation as indicated to find the resulting set. \(U=\{a, b, c, \ldots, z\}, S=\{s, a, m, p, l, e\}, M=\{m, a, p\}, L=\{l, a, m, p\}, D=\{d, o, g\}\), and \(P=\{p, l, o, t\}\).
Find the set consisting of elements in \(P\) or \(M\).Use the sets provided to apply the "AND" or "OR" operation as indicated to find the resulting set. \(U=\{a, b, c, \ldots, z\}, S=\{s, a, m, p, l, e\}, M=\{m, a, p\}, L=\{l, a, m, p\}, D=\{d, o, g\}\), and \(P=\{p, l, o, t\}\).
Find the set consisting of elements in \(M\) and \(D\).Use the sets provided to apply the "AND" or "OR" operation as indicated to find the resulting set. \(U=\{a, b, c, \ldots, z\}, S=\{s, a, m, p, l, e\}, M=\{m, a, p\}, L=\{l, a, m, p\}, D=\{d, o, g\}\), and \(P=\{p, l, o, t\}\).
Find the set consisting of elements in \(L\) and \(M\).Use the sets provided to apply the "AND" or "OR" operation as indicated to find the resulting set. \(U=\{a, b, c, \ldots, z\}, S=\{s, a, m, p, l, e\}, M=\{m, a, p\}, L=\{l, a, m, p\}, D=\{d, o, g\}\), and \(P=\{p, l, o, t\}\).
Find the set consisting of elements in \(L\) or \(M\).Use the sets provided to apply the "AND" or "OR" operation as indicated to find the resulting set. \(U=\{a, b, c, \ldots, z\}, S=\{s, a, m, p, l, e\}, M=\{m, a, p\}, L=\{l, a, m, p\}, D=\{d, o, g\}\), and \(P=\{p, l, o, t\}\).
Find the set consisting of the elements in \(D\) or \(M\) or \(P\).Use the sets provided to apply the "AND" or "OR" operation as indicated to find the resulting set. \(U=\{a, b, c, \ldots, z\}, S=\{s, a, m, p, l, e\}, M=\{m, a, p\}, L=\{l, a, m, p\}, D=\{d, o, g\}\), and \(P=\{p, l, o, t\}\).
Find the set consisting of the elements in \(S\) or \(M\) or \(P\).Use the sets provided to apply the "AND" or "OR" operation as indicated to find the resulting set. \(U=\{a, b, c, \ldots, z\}, S=\{s, a, m, p, l, e\}, M=\{m, a, p\}, L=\{l, a, m, p\}, D=\{d, o, g\}\), and \(P=\{p, l, o, t\}\).
Find the set consisting of the elements in ( \(S\) or \(D\) ) and \(P\).Use the sets provided to apply the "AND" or "OR" operation as indicated to find the resulting set. \(U=\{a, b, c, \ldots, z\}, S=\{s, a, m, p, l, e\}, M=\{m, a, p\}, L=\{l, a, m, p\}, D=\{d, o, g\}\), and \(P=\{p, l, o, t\}\).
Find the set consisting of the elements in \(S\) or ( \(D\) and \(P\) ).Use the sets provided to apply the "AND" or "OR" operation as indicated to find the resulting set. \(U=\{a, b, c, \ldots, z\}, S=\{s, a, m, p, l, e\}, M=\{m, a, p\}, L=\{l, a, m, p\}, D=\{d, o, g\}\), and \(P=\{p, l, o, t\}\).
Find the set consisting of elements in \(U\) or \((P\) and \(S)\).Use the sets provided to apply the "AND" or "OR" operation as indicated to find the resulting set. \(U=\{a, b, c, \ldots, z\}, S=\{s, a, m, p, l, e\}, M=\{m, a, p\}, L=\{l, a, m, p\}, D=\{d, o, g\}\), and \(P=\{p, l, o, t\}\).
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