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mathematics
contemporary mathematics
Contemporary Mathematics 1st Edition OpenStax - Solutions
Set \(A=\{h, a, p, y\}\) and set \(B=\{s, a, d\}\). Find \(A\) union \(B\).
Set \(A=\{\) red, yellow, blue \(\}\) and set \(B=\{\) orange, green, purple \(\}\). Find \(A \cup B\).
Set \(A=\{a, b, c, \ldots, z\}\) and set \(B=\{a, e, i, o, u\}\). Find \(A \cup B\).
If \(n(A)=23, n(B)=17\), and \(n(A \cap B)=7\), then find \(n(A \cup B)\).
If \(A \cap B=\varnothing, n(A)=35\), and \(n(B)=78\), then find \(n(A \cup B)\).
\(A=\{h, a, p, y\}\), and \(B=\{a, w, e, s, o, m\}\), and \(C=\{m, a, t, h\}\).Find the set consisting of elements in:1. \(A\) or \(B\).2. \(A\) and \(C\).3. \(B\) or \(C\).4. \((A\) and \(C)\) and \(B\).
Ravi and Priya are serving soup and salad along with the main course at their wedding reception. The reception will have a total of 150 guests in attendance. A total of 92 soups and 85 salads were ordered, while 23 guests did not order any soup or salad.1. How many guests had soup or salad or
1. Find \(A \cap B\).2. Find \(A \cup B\).3. Find \(A \cap B^{\prime}\).4. Find \(n\left(A \cap B^{\prime}\right)\). U={0, 1, 2, 3, 4, 5, 6, 7, 8, 9} B A 1 2 5 7 8 00 6 Venn diagram with two intersecting sets and members.
1. Find \(n(A\) or \(B)\).2. Find \(n(A\) and \(B)\).3. Find \(n\left(A^{\prime}\right)\). U A 23 17 10 Venn diagram with two disjoint sets and number of elements in each section.
Use the same Venn diagram in the example above to answer the following questions.1. How many people donated blood with a type B blood factor?2. How many people who donated blood did not have a type \(B\) blood factor?3. How many people who donated blood had a type B blood factor or were
A group of 50 people attending a conference who preordered their lunch were able to select their choice of soup, salad, or sandwich. A total of 17 people selected soup, 29 people selected salad and 35 people selected a sandwich. Of these orders, 11 attendees selected soup and salad, 10 attendees
Using the same sets from Example 1.37, perform the set operations indicated.1. Find \(A \cap(B \cap C)\).2. Find \((A \cap B) \cup(A \cap C)\).3. Find \(\left(A \cup C^{\prime}\right) \cap\left(B \cup C^{\prime}\right)\)Data from Example 1.37Perform the set operations as indicated on the following
De Morgan's Law for the complement of the intersection of two sets \(A\) and \(B\) states that \((A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}\). Use a Venn diagram to prove that De Morgan's Law is true.
Determine whether the following collection describes a well-defined set: "A group of small tomatoes."
\(\{1,5,9, \ldots\}\)Classify each of the following sets as either finite or infinite.
\(\{c \mid c\) is a cat \(\}\)Classify each of the following sets as either finite or infinite.
\(\{1,2,3, \ldots, 1000\}\)Classify each of the following sets as either finite or infinite.
\(\{s, m, i, l, e\}\)Classify each of the following sets as either finite or infinite.
\(\left\{m \in \mathbb{N} \mid m=n^{2}\right.\) where \(n\) is a natural number \(\}\)Classify each of the following sets as either finite or infinite.
Find \(A\) or \(B\).Use the sets provided to answer the following questions: \(U=\{31,32,33, \ldots, 50\}, A=\{35,38,41,44,47,50\}\), \(B=\{32,36,40,44,48\}\), and \(C=\{31,32,41,42,48,50\}\).
Find \(B\) and \(C\).Use the sets provided to answer the following questions: \(U=\{31,32,33, \ldots, 50\}, A=\{35,38,41,44,47,50\}\), \(B=\{32,36,40,44,48\}\), and \(C=\{31,32,41,42,48,50\}\).
Determine if set \(A\) is equivalent to, equal to, or neither equal nor equivalent to set \(C\). Justify your answer.Use the sets provided to answer the following questions: \(U=\{31,32,33, \ldots, 50\}, A=\{35,38,41,44,47,50\}\), \(B=\{32,36,40,44,48\}\), and \(C=\{31,32,41,42,48,50\}\).
Find \(n(A \cup C)\).Use the sets provided to answer the following questions: \(U=\{31,32,33, \ldots, 50\}, A=\{35,38,41,44,47,50\}\), \(B=\{32,36,40,44,48\}\), and \(C=\{31,32,41,42,48,50\}\).
Find \(A \cap(B \cap C)\).Use the sets provided to answer the following questions: \(U=\{31,32,33, \ldots, 50\}, A=\{35,38,41,44,47,50\}\), \(B=\{32,36,40,44,48\}\), and \(C=\{31,32,41,42,48,50\}\).
Find \((A \cup B)^{\prime} \cap C\).Use the sets provided to answer the following questions: \(U=\{31,32,33, \ldots, 50\}, A=\{35,38,41,44,47,50\}\), \(B=\{32,36,40,44,48\}\), and \(C=\{31,32,41,42,48,50\}\).
Find \(\left(A \cap B^{\prime}\right) \cup C\).Use the sets provided to answer the following questions: \(U=\{31,32,33, \ldots, 50\}, A=\{35,38,41,44,47,50\}\), \(B=\{32,36,40,44,48\}\), and \(C=\{31,32,41,42,48,50\}\).
Find \(B^{\prime}\).Use the Venn diagram below to answer the following questions. \(U=\{g, o, l, d, e, n\}\) A n e d g B
Find \(A \cup B\).Use the Venn diagram below to answer the following questions. \(U=\{g, o, l, d, e, n\}\) A n e d g B
Find \(A \cap B^{\prime}\).Use the Venn diagram below to answer the following questions. \(U=\{g, o, l, d, e, n\}\) A n e d g B
Draw a Venn diagram to represent the relationship between the two sets: "All flowers are plants."Use the Venn diagram below to answer the following questions. \(U=\{g, o, l, d, e, n\}\) A n e d g B
Find the number of donors who were \(\mathrm{O}^{-}\); that is, find \(n\left(\left(A \cup B \cup R h^{+}\right)^{\prime}\right)\).For the following questions, use the Venn diagram showing the blood types of all donors at a recent mobile blood drive. Donors 128 A 7 40 3 12 47 5 B Rh+
Find the number of donors who were \(\mathrm{A}^{+}\)or \(\mathrm{B}^{+}\)or \(\mathrm{AB}^{+}\).For the following questions, use the Venn diagram showing the blood types of all donors at a recent mobile blood drive. Donors 128 A 7 40 3 12 47 5 B Rh+
Use Venn diagrams to prove that if \(A \subset B\), then \(A \cap B=A\).For the following questions, use the Venn diagram showing the blood types of all donors at a recent mobile blood drive. Donors 128 A 7 40 3 12 47 5 B Rh+
A ___________ is a well-defined collection of distinct objects.
A collection of well-defined objects without any members in it is called the ____________.
Write the set consisting of the last five letters of the English alphabet using the roster method.
Write the set consisting of the numbers 1 through 20 inclusive using the roster method and an ellipsis.
Write the set of all zebras that do not have stripes in symbolic form.
Write the set of negative integers using the roster method and an ellipsis.
Use set builder notation to write the set of all even integers.
Write the set of all letters in the word Mississippi and label it with a capital \(M\).
Determine whether the following collection describes a well-defined set: "A group of these five types of apples: Granny Smith, Red Delicious, McIntosh, Fuji, and Jazz."
Determine whether the following collection describes a well-defined set: "A group of five large dogs."
Determine the cardinality of the set \(A=\{\) Alabama, Alaska, Arkansas, Arizona \(\}\).
Determine whether the following set is a finite set or an infinite set: \(F=\{5,10,15, \ldots\}\).
Determine whether sets \(A\) and \(B\) are equal, equivalent, or neither: \(A=\{a, b, c\}\) and \(B=\{1,2,3,4\}\).
Determine if sets \(A\) and \(B\) are equal, equivalent, or neither: \(A=\{a, b, c\}\) and \(B=\{c, a, b\}\).
Determine if sets \(A\) and \(B\) are equal, equivalent, or neither: \(A=\{a, b, c\}\) and \(B=\{1,2,3\}\).
If every member of set \(A\) is also a member of set \(B\), then set \(A\) is a ________ of set \(B\).
Determine whether set \(A\) is a subset, proper subset, or neither a subset nor proper subset of set \(B\) : \(A=\{s, o, n\}\) and \(B=\{s, o, n, g\}\).
Determine whether set \(A\) is a subset, proper subset, or neither a subset nor proper subset of set \(B\) : \(A=\{s, o, n\}\) and \(B=\{s, o, l\}\).
Determine whether set \(A\) is a subset, proper subset, or neither a subset nor proper subset of set \(B: A=\{s, o, n\}\) and \(B=\{o, n, s\}\).
List all the subsets of the set {up, down}.
List all the subsets of the set \(\{0\}\).
Calculate the total number of subsets of the set { Scooby, Velma, Daphne, Shaggy, Fred}.
Calculate the total number of subsets of the set {top hat, thimble, iron, shoe, battleship, cannon}.
Find a subset of the set \(\{g, r, e, a, t\}\) that is equivalent, but not equal, to {t, e, a}.
Find a subset of the set \(\{g, r, e, a, t\}\) that is equal to \(\{t, e, a\}\).
Find two equivalent finite subsets of the set of natural numbers, \(\mathbb{N}=\{1,2,3, \ldots\}\), with a cardinality of 4 .
Find two equal finite subsets of the set of natural numbers, \(\mathbb{N}=\{1,2,3, \ldots\}\), with a cardinality of 3 .
Use the Venn diagram below to describe the relationship between the sets, symbolically and in words: \(U=\) Trees E = Elms
Use the Venn diagram below to describe the relationship between the sets, symbolically and in words: \(U=\) Modes of Transportation Planes Trains
Draw a Venn diagram to represent the relationship between the described sets: Falcons \(\subset\) Raptors.
Draw a Venn diagram to represent the relationship between the described sets: Natural numbers \(\subset\) Integers \(\subset\) Real numbers.
The universal set is the set \(U=\{s, m, i, l, e\}\). Find the complement of the set \(E=\{e, l, m\}\).
The universal set is the set \(U=\{1,2,3, \ldots\}\). Find the complement of the set \(V=\{18,19,20, \ldots\}\).
Use the Venn diagram below to determine the members of the set \(A^{\prime}\). \(U=\{r, e, a, d, i, n, g\}\) A {d, e, a, r}
Use the Venn diagram below to determine the members of the set \(A^{\prime}\). \(U=\{r, e, a, d, i, n, g\}\) {g, r, a, n, d} A
What is \(S \cap R\) ?Determine the union and intersection of the sets indicated: \(U=\{a, b, c, \ldots, z\}, S=\{s, c, r, a, b, l, e\}, B=\{b, r, a, c, e\}\), \(C=\{c, r, a, b\}, R=\{r, i, s, k\}\), and \(Q=\{q, u, i, z\}\).
What is \(S \cup B\) ?Determine the union and intersection of the sets indicated: \(U=\{a, b, c, \ldots, z\}, S=\{s, c, r, a, b, l, e\}, B=\{b, r, a, c, e\}\), \(C=\{c, r, a, b\}, R=\{r, i, s, k\}\), and \(Q=\{q, u, i, z\}\).
Write the set containing the elements in sets \(B\) or \(Q\).Determine the union and intersection of the sets indicated: \(U=\{a, b, c, \ldots, z\}, S=\{s, c, r, a, b, l, e\}, B=\{b, r, a, c, e\}\), \(C=\{c, r, a, b\}, R=\{r, i, s, k\}\), and \(Q=\{q, u, i, z\}\).
Write the set containing all the elements is both sets \(B\) and \(Q\).Determine the union and intersection of the sets indicated: \(U=\{a, b, c, \ldots, z\}, S=\{s, c, r, a, b, l, e\}, B=\{b, r, a, c, e\}\), \(C=\{c, r, a, b\}, R=\{r, i, s, k\}\), and \(Q=\{q, u, i, z\}\).
Find \(C\) intersection \(R\).Determine the union and intersection of the sets indicated: \(U=\{a, b, c, \ldots, z\}, S=\{s, c, r, a, b, l, e\}, B=\{b, r, a, c, e\}\), \(C=\{c, r, a, b\}, R=\{r, i, s, k\}\), and \(Q=\{q, u, i, z\}\).
Find \(C\) union \(R\).Determine the union and intersection of the sets indicated: \(U=\{a, b, c, \ldots, z\}, S=\{s, c, r, a, b, l, e\}, B=\{b, r, a, c, e\}\), \(C=\{c, r, a, b\}, R=\{r, i, s, k\}\), and \(Q=\{q, u, i, z\}\).
Find the cardinality of \(C \cup R, n(C \cup R)\).Determine the union and intersection of the sets indicated: \(U=\{a, b, c, \ldots, z\}, S=\{s, c, r, a, b, l, e\}, B=\{b, r, a, c, e\}\), \(C=\{c, r, a, b\}, R=\{r, i, s, k\}\), and \(Q=\{q, u, i, z\}\).
Find \(n(S\) union \(R)\).Determine the union and intersection of the sets indicated: \(U=\{a, b, c, \ldots, z\}, S=\{s, c, r, a, b, l, e\}, B=\{b, r, a, c, e\}\), \(C=\{c, r, a, b\}, R=\{r, i, s, k\}\), and \(Q=\{q, u, i, z\}\).
Use the Venn diagram below to find \(A \cap B\). U={a, b, c,, z} A d a k e B
Use the Venn diagram below to find \(n(A \cup B)\). \(U=24\) A 5 7 2 B 10
Find \(n(A \cup C)\).Use the Venn diagram below to answer the following questions.\(U=47\) A 7 5 2 00 8 C 12 3 B 6
Find \(n(B \cap C)\).Use the Venn diagram below to answer the following questions.\(U=47\) A 7 5 2 00 8 C 12 3 B 6
A food truck owner surveyed a group of 50 customers about their preferences for hamburger condiments. After tallying the responses, the owner found that 24 customers preferred ketchup, 11 preferred mayonnaise, and 31 preferred mustard. Of these customers, eight preferred ketchup and mayonnaise, one
Given \(U=\{\mathrm{r}, \mathrm{s}, \mathrm{t}, 1, \mathrm{n}, \mathrm{e}, \mathrm{i}, \mathrm{a}\}, R=\{\mathrm{r}, \mathrm{e}, \mathrm{s}, \mathrm{t}\}, S=\{\mathrm{s}, \mathrm{t}, \mathrm{a}, \mathrm{i}, \mathrm{r}\}\), and \(L=\{1, \mathrm{i}, \mathrm{n}, \mathrm{e}, \mathrm{s}\}\), find \((S
Use Venn diagrams to prove that if \(A \subset B\), then \(B^{\prime} \subset A^{\prime}\).Use the Venn diagram below to answer the following questions.\(U=47\) A 7 5 2 00 8 C 12 3 B 6
How many gamers club members play all three types of games: board games, card games, and video games?A gamers club at Baily Middle School consisting of 25 members was surveyed to find out who played board games, card games, or video games. Use the results depicted in the Venn diagram below to
How many gamers are in the set Board \(\cap\) Video?A gamers club at Baily Middle School consisting of 25 members was surveyed to find out who played board games, card games, or video games. Use the results depicted in the Venn diagram below to answer the following exercises.Gamers Club Members
If Javier is in the region with a total of three members, what type of games does he play?A gamers club at Baily Middle School consisting of 25 members was surveyed to find out who played board games, card games, or video games. Use the results depicted in the Venn diagram below to answer the
How many gamers play video games?A gamers club at Baily Middle School consisting of 25 members was surveyed to find out who played board games, card games, or video games. Use the results depicted in the Venn diagram below to answer the following exercises.Gamers Club Members \(=25\) Board 1 10 10
How many gamers are in the set Board \(\cup\) Card?A gamers club at Baily Middle School consisting of 25 members was surveyed to find out who played board games, card games, or video games. Use the results depicted in the Venn diagram below to answer the following exercises.Gamers Club Members
How many members of the gamers club do not play video games?A gamers club at Baily Middle School consisting of 25 members was surveyed to find out who played board games, card games, or video games. Use the results depicted in the Venn diagram below to answer the following exercises.Gamers Club
How many members of this club only play board games?A gamers club at Baily Middle School consisting of 25 members was surveyed to find out who played board games, card games, or video games. Use the results depicted in the Venn diagram below to answer the following exercises.Gamers Club Members
How many members of this club only play video games?A gamers club at Baily Middle School consisting of 25 members was surveyed to find out who played board games, card games, or video games. Use the results depicted in the Venn diagram below to answer the following exercises.Gamers Club Members
How many members of the gamers club play video and card games?A gamers club at Baily Middle School consisting of 25 members was surveyed to find out who played board games, card games, or video games. Use the results depicted in the Venn diagram below to answer the following exercises.Gamers Club
How many members of the gamers club are in the set Card'?A gamers club at Baily Middle School consisting of 25 members was surveyed to find out who played board games, card games, or video games. Use the results depicted in the Venn diagram below to answer the following exercises.Gamers Club
Blood type \(\mathrm{AB}^{+}\)is the universal acceptor. Of the 140 people who donated at City Honors, how many had blood type \(\mathrm{AB}^{+}\)?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
Blood type \(\mathrm{O}^{-}\)is the universal donor. Anyone needing a blood transfusion can receive this blood type. How many people who donated blood during this drive had \(\mathrm{O}^{-}\)blood?A blood drive at City Honors High School recently collected blood from 140 students, staff, and
How many people donated with a type A blood factor?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
How many people donated with a type \(A\) and type \(B\) blood factor (that is, they had type \(A B\) blood).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.
How many donors were \(\mathrm{O}^{+}\)?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
How many donors were not \(\mathrm{Rh}^{+}\)?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
Opal has blood type \(\mathrm{A}^{+}\). If she needs to have surgery that requires a blood transfusion, she can accept blood from anyone who does not have a type B blood factor. How many people donated blood during this drive at City Honors that Opal can accept?A blood drive at City Honors High
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