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mathematics
contemporary mathematics
Contemporary Mathematics 1st Edition OpenStax - Solutions
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 \(P=\{p, l, o, t\}\).
Find \(A \cup B\).Use the Venn diagram provided to answer the following questions about the sets. \(U=\{a, b, c, \ldots, z\}\) B a A b a C d
Find \(A \cap B\).Use the Venn diagram provided to answer the following questions about the sets. \(U=\{a, b, c, \ldots, z\}\) B a A b a C d
Find \((A \cap B)^{\prime}\)Use the Venn diagram provided to answer the following questions about the sets. \(U=\{a, b, c, \ldots, z\}\) B a A b a C d
Find \((A \cup B)^{\prime}\).Use the Venn diagram provided to answer the following questions about the sets. \(U=\{a, b, c, \ldots, z\}\) B a A b a C d
Find \(A \cap B^{\prime}\).Use the Venn diagram provided to answer the following questions about the sets. \(U=\{a, b, c, \ldots, z\}\) B a A b a C d
Find \(B \cap A^{\prime}\).Use the Venn diagram provided to answer the following questions about the sets. \(U=\{a, b, c, \ldots, z\}\) B a A b a C d
Find \(A \cap B\).Use the Venn diagram provided to answer the following questions about the sets. \(U=\{a, b, c, \ldots, z\}\) b B A p C S
Find \(A \cup B\).Use the Venn diagram provided to answer the following questions about the sets. \(U=\{a, b, c, \ldots, z\}\) b B A p C S
Find \((A \cup B)^{\prime}\).Use the Venn diagram provided to answer the following questions about the sets. \(U=\{a, b, c, \ldots, z\}\) b B A p C S
Find \((A \cap B)^{\prime}\).Use the Venn diagram provided to answer the following questions about the sets. \(U=\{a, b, c, \ldots, z\}\) b B A p C S
Find \(B \cap A^{\prime}\).Use the Venn diagram provided to answer the following questions about the sets. \(U=\{a, b, c, \ldots, z\}\) b B A p C S
Find \(A \cap B^{\prime}\).Use the Venn diagram provided to answer the following questions about the sets. \(U=\{a, b, c, \ldots, z\}\) b B A p C S
Find \(A \cup B\).Use the Venn diagram provided to answer the following questions about the sets. \(U=Z=\{\ldots,-2,-1,0,1,2, \ldots\}\) B A (1, 2, 3, ...)
Find \(A \cap B\).Use the Venn diagram provided to answer the following questions about the sets. \(U=Z=\{\ldots,-2,-1,0,1,2, \ldots\}\) B A (1, 2, 3, ...)
Find \((A \cup B)^{\prime}\).Use the Venn diagram provided to answer the following questions about the sets. \(U=Z=\{\ldots,-2,-1,0,1,2, \ldots\}\) B A (1, 2, 3, ...)
Find \((A \cap B)^{\prime}\).Use the Venn diagram provided to answer the following questions about the sets. \(U=Z=\{\ldots,-2,-1,0,1,2, \ldots\}\) B A (1, 2, 3, ...)
Find \(B \cap A^{\prime}\).Use the Venn diagram provided to answer the following questions about the sets. \(U=Z=\{\ldots,-2,-1,0,1,2, \ldots\}\) B A (1, 2, 3, ...)
Find \(A \cap B^{\prime}\).Use the Venn diagram provided to answer the following questions about the sets. \(U=Z=\{\ldots,-2,-1,0,1,2, \ldots\}\) B A (1, 2, 3, ...)
If set \(A=\{\) red, white, blue \(\}\) and set \(B=\{\) green, white, red \(\}\), find \(n(A \cup B)\).Determine the cardinality of the union of set \(A\) and set \(B\).
If set \(A=\{\) silver, gold, bronze \(\}\) and set \(B=\{\) silver, gold \(\}\), find the number of elements in \(A\) or \(B\).Determine the cardinality of the union of set \(A\) and set \(B\).
If set \(A=\{\) glass, plate, fork, knife \(\}\) and set \(B=\{\) bowl, spoon, cup \(\}\), find the number of elements in \(A\) or \(B\).Determine the cardinality of the union of set \(A\) and set \(B\).
If set \(A=\{\) Algebra, Geometry, Biology, Physics, Chemistry, English \(\}\) and Set \(B=\{\) Algebra, English, History, Spanish, French, Music \(\}\), find \(n(A \cup B)\).Determine the cardinality of the union of set \(A\) and set \(B\).
Use the Venn diagram to determine the cardinality of \(A\) union \(B\). U = 21 A 2 7 8 B
Use the Venn diagram to determine the cardinality of \(A\) union \(B\). U=15 A 3 10 B
Use the Venn diagram to determine the cardinality of \(A\) union \(B\). U=88 B 52 A 22
Use the Venn diagram to determine the cardinality of \(A\) union \(B\). U=44 A 15 18 4 B
A ____________ is a well-defined collection of objects.
The ____________ of a finite set \(A\), denoted \(n(A)\), is the number of elements in set \(A\).
Determine if the following description describes a well-defined set: "The top 5 pizza restaurants in Chicago."
The United States is the only country to have landed people on the moon as of March 21, 2021. What is the cardinality of the set of all people who have walked on the moon prior to this date?
Set \(A\) is a set of a dozen distinct donuts, and set \(B\) is a set of a dozen different types of apples. Is set \(A\) equal to set \(B\), equivalent to set \(B\), or neither?
Is the set of all butterflies in the world a finite set or an infinite set?
Represent the set of all upper-case letters of the English alphabet using both the roster method and set builder notation.
Every member of a ____________ of a set is also a member of the set.
Explain what distinguishes a proper subset of a set from a subset of a set.
The ____________ set is a proper subset of every set except itself.
Is the following statement true or false? \(A \subseteq A\).
If the cardinality of set \(A\) is \(n(A)=10\), then set \(A\) has a total of ____________ subsets.
Set \(A\) is ____________ to set \(B\) if \(n(A)=n(B)\).
If every member of set \(A\) is a member of set \(B\) and every member of set \(B\) is also a member set \(A\), then set \(A\) is ______________ to set \(B\).
A Venn diagram is a graphical representation of the ______________ between sets.
In a Venn diagram, the set of all data under consideration, the ______________ set, is drawn as a rectangle.
Two sets that do not share any elements in common are ______________ sets.
The ___________ of a subset \(A\) or the universal set, \(U\), is the set of all members of \(U\) that are not in \(A\).
The sets \(A\) and \(A^{\prime}\) are ______________ subsets of the universal set.
The ______________ of two sets \(A\) and \(B\) is the set of all elements that they share in common.
The ______________ of two sets \(A\) and \(B\) is the collection of all elements that are in set \(A\) or set \(B\), or both set \(A\) and set B.
The union of two sets \(A\) and \(B\) is represented symbolically as \( \qquad \) .
The intersection of two sets \(A\) and \(B\) is represented symbolically as \( \qquad \) .
If set \(A\) is a subset of set \(B\), then \(A\) intersection \(B\) is equal to set \( \qquad \)
If set \(A\) is a subset of set \(B\), then \(A\) union \(B\) is equal to set \( \qquad \)
If set \(A\) and set \(B\) are disjoint sets, then \(A\) intersection \(B\) is the ______________ set.
The cardinality of \(A\) union \(B, n(A \cup B)\), is found using the formula: \( \qquad \)
When creating a Venn diagram with two or more subsets, you should begin with the region involving the most ______________ , then work your way from the center outward.
To construct a Venn diagram with three subsets, draw and label three circles that overlap in a common ______________ region inside the rectangle of the universal set to represent each of the three subsets.
In a Venn diagram with three sets, the area where all three sets, \(A, B\), and \(C\) overlap is equal to the set \( \qquad \)
When performing set operations with three or more sets, the order of operations is inner most ______________ first, then find the ______________ of any sets, and finally perform any union or intersection operations that remain.
To prove set equality using Venn diagrams, draw a Venn diagram to represent each side of the ______________ and then compare the diagrams to determine if they match or not. If they match, the statement is ______________, otherwise it is not.
chocolate, vanilla, strawberryFor the following exercises, list all the proper subsets of each set.
true, falseFor the following exercises, list all the proper subsets of each set.
\(\{\) mother, father, daughter, son \(\}\)For the following exercises, list all the proper subsets of each set.
\(\{7\}\)For the following exercises, list all the proper subsets of each set.
\(D\) and \(A\)For the following exercises, determine the relationship between the two sets and write the relationship symbolically.\(D=\{0,1,2, \ldots, 9\}, A=\{0,2,4,6,8\}, B=\{1,3,5,7,9\}, C=\{8,6,4,2,0\}, Z=\{0\}\), and \(\varnothing\)
\(B\) and \(D\)For the following exercises, determine the relationship between the two sets and write the relationship symbolically.\(D=\{0,1,2, \ldots, 9\}, A=\{0,2,4,6,8\}, B=\{1,3,5,7,9\}, C=\{8,6,4,2,0\}, Z=\{0\}\), and \(\varnothing\)
\(C\) and \(D\)For the following exercises, determine the relationship between the two sets and write the relationship symbolically.\(D=\{0,1,2, \ldots, 9\}, A=\{0,2,4,6,8\}, B=\{1,3,5,7,9\}, C=\{8,6,4,2,0\}, Z=\{0\}\), and \(\varnothing\)
\(Z\) and \(C\)For the following exercises, determine the relationship between the two sets and write the relationship symbolically.\(D=\{0,1,2, \ldots, 9\}, A=\{0,2,4,6,8\}, B=\{1,3,5,7,9\}, C=\{8,6,4,2,0\}, Z=\{0\}\), and \(\varnothing\)
\(Z\) and \(\varnothing\)For the following exercises, determine the relationship between the two sets and write the relationship symbolically.\(D=\{0,1,2, \ldots, 9\}, A=\{0,2,4,6,8\}, B=\{1,3,5,7,9\}, C=\{8,6,4,2,0\}, Z=\{0\}\), and \(\varnothing\)
\(A\) and \(B\)For the following exercises, determine the relationship between the two sets and write the relationship symbolically.\(D=\{0,1,2, \ldots, 9\}, A=\{0,2,4,6,8\}, B=\{1,3,5,7,9\}, C=\{8,6,4,2,0\}, Z=\{0\}\), and \(\varnothing\)
\(A\) and \(C\)For the following exercises, determine the relationship between the two sets and write the relationship symbolically.\(D=\{0,1,2, \ldots, 9\}, A=\{0,2,4,6,8\}, B=\{1,3,5,7,9\}, C=\{8,6,4,2,0\}, Z=\{0\}\), and \(\varnothing\)
\(\varnothing\) and \(D\)For the following exercises, determine the relationship between the two sets and write the relationship symbolically.\(D=\{0,1,2, \ldots, 9\}, A=\{0,2,4,6,8\}, B=\{1,3,5,7,9\}, C=\{8,6,4,2,0\}, Z=\{0\}\), and \(\varnothing\)
\(B\) and \(C\)For the following exercises, determine the relationship between the two sets and write the relationship symbolically.\(D=\{0,1,2, \ldots, 9\}, A=\{0,2,4,6,8\}, B=\{1,3,5,7,9\}, C=\{8,6,4,2,0\}, Z=\{0\}\), and \(\varnothing\)
\(A\) and \(Z\)For the following exercises, determine the relationship between the two sets and write the relationship symbolically.\(D=\{0,1,2, \ldots, 9\}, A=\{0,2,4,6,8\}, B=\{1,3,5,7,9\}, C=\{8,6,4,2,0\}, Z=\{0\}\), and \(\varnothing\)
\(\{\) Adele, Beyonce, Cher, Madonna, Shakira \}For the following exercises, calculate the total number of subsets of each set.
\(\{\) Art, Paul \(\}\)For the following exercises, calculate the total number of subsets of each set.
Peter, Paul, MaryFor the following exercises, calculate the total number of subsets of each set.
\(\varnothing\)For the following exercises, calculate the total number of subsets of each set.For the following exercises, calculate the total number of subsets of each set.
\(\{3\}\)For the following exercises, calculate the total number of subsets of each set.
\(\{l, o, v, e\}\)For the following exercises, calculate the total number of subsets of each set.
{ }For the following exercises, calculate the total number of subsets of each set.
football, baseball, basketball, soccer, hockey, tennis, golfFor the following exercises, calculate the total number of subsets of each set.
Set \(A\), if \(n(A)=12\).For the following exercises, calculate the total number of subsets of each set.
Set \(B\), if \(n(B)=9\).For the following exercises, calculate the total number of subsets of each set.
Find a subset of \(U\) that is equivalent, but not equal, to the set: \(\{1, \mathrm{a}, \mathrm{s}, \mathrm{t}\}\).For the following exercises, use the set of letters in the word largest as the set, \(U=\{1, \mathrm{a}, \mathrm{r}, \mathrm{g}, \mathrm{e}, \mathrm{s}, \mathrm{t}\}\).
Find a subset of \(U\) that is equal to the set: \(\{1, \mathrm{a}, \mathrm{s}, \mathrm{t}\}\).For the following exercises, use the set of letters in the word largest as the set, \(U=\{1, \mathrm{a}, \mathrm{r}, \mathrm{g}, \mathrm{e}, \mathrm{s}, \mathrm{t}\}\).
Find a subset of \(U\) that is equal to the set: \(\{\mathrm{a}, \mathrm{r}, \mathrm{t}\}\).For the following exercises, use the set of letters in the word largest as the set, \(U=\{1, \mathrm{a}, \mathrm{r}, \mathrm{g}, \mathrm{e}, \mathrm{s}, \mathrm{t}\}\).
Find a subset of \(U\) that is equivalent, but not equal, to the set \(\{\mathrm{a}, \mathrm{r}, \mathrm{t}, \mathrm{s}\}\).For the following exercises, use the set of letters in the word largest as the set, \(U=\{1, \mathrm{a}, \mathrm{r}, \mathrm{g}, \mathrm{e}, \mathrm{s}, \mathrm{t}\}\).
Find a subset of \(U\) that is equivalent, but not equal, to the set: \(\{\mathrm{r}, \mathrm{a}, \mathrm{t}, \mathrm{e}, \mathrm{s}\}\).For the following exercises, use the set of letters in the word largest as the set, \(U=\{1, \mathrm{a}, \mathrm{r}, \mathrm{g}, \mathrm{e}, \mathrm{s},
Find a subset of \(U\) that is equal to the set: \(\{\mathrm{r}, \mathrm{a}, \mathrm{t}, \mathrm{e}, \mathrm{s}\}\).For the following exercises, use the set of letters in the word largest as the set, \(U=\{1, \mathrm{a}, \mathrm{r}, \mathrm{g}, \mathrm{e}, \mathrm{s}, \mathrm{t}\}\).
Find two three-character subsets of set \(U\) that are equivalent, but not equal, to each other.For the following exercises, use the set of letters in the word largest as the set, \(U=\{1, \mathrm{a}, \mathrm{r}, \mathrm{g}, \mathrm{e}, \mathrm{s}, \mathrm{t}\}\).
Find two three-character subsets of set \(U\) that are equal to each other.For the following exercises, use the set of letters in the word largest as the set, \(U=\{1, \mathrm{a}, \mathrm{r}, \mathrm{g}, \mathrm{e}, \mathrm{s}, \mathrm{t}\}\).
Find two five-character subsets of set \(U\) that are equal to each other.For the following exercises, use the set of letters in the word largest as the set, \(U=\{1, \mathrm{a}, \mathrm{r}, \mathrm{g}, \mathrm{e}, \mathrm{s}, \mathrm{t}\}\).
Find two five-character subsets of set \(U\) that are equivalent, but not equal, to each other.For the following exercises, use the set of letters in the word largest as the set, \(U=\{1, \mathrm{a}, \mathrm{r}, \mathrm{g}, \mathrm{e}, \mathrm{s}, \mathrm{t}\}\).
Find two equivalent subset of \(U\) with a cardinality of 7 .For the following exercises, use the set of integers as the set \(U=\mathbb{Z}=\{\ldots,-2,-1,0,1,2, \ldots\}\).
Find two equal subsets of \(U\) with a cardinality of 4 .For the following exercises, use the set of integers as the set \(U=\mathbb{Z}=\{\ldots,-2,-1,0,1,2, \ldots\}\).
Find a subset of \(U\) that is equivalent, but not equal to, \(\{0,3,6,9, \ldots\}\).For the following exercises, use the set of integers as the set \(U=\mathbb{Z}=\{\ldots,-2,-1,0,1,2, \ldots\}\).
Find a subset of \(U\) that is equivalent, but not equal to, \(\{-1,-4,-9,-16,-25, \ldots\}\).For the following exercises, use the set of integers as the set \(U=\mathbb{Z}=\{\ldots,-2,-1,0,1,2, \ldots\}\).
True or False. The set of natural numbers, \(\mathbb{N}=\{1,2,3, \ldots\}\), is equivalent to set \(U\).For the following exercises, use the set of integers as the set \(U=\mathbb{Z}=\{\ldots,-2,-1,0,1,2, \ldots\}\).
True or False. Set \(U\) is an equivalent subset of the set of rational numbers, \(\mathbb{Q}=\left\{\left.\frac{p}{q} \rightvert\, p\right.\) and \(q\) are integers and \(\left.q eq 0.\right\}\).For the following exercises, use the set of integers as the set \(U=\mathbb{Z}=\{\ldots,-2,-1,0,1,2,
Write a set consisting of your three favorite sports and label it with a capital \(S\).
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