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mathematics
contemporary mathematics
Contemporary Mathematics 1st Edition OpenStax - Solutions
For each of the following collections, determine if it represents a well-defined set.1. The group of all past vice presidents of the United States.2. A group of old cats.
Represent each of the following sets symbolically.1. The set of prime numbers less than 2 .2. The set of birds that are also mammals.
Write the set of even natural numbers including and between 2 and 100 , and label it with a capital \(E\). Include an ellipsis.
Write the set of integers using the roster method, and label it with a \(\mathbb{Z}\).
Using set builder notation, write the set \(B\) of all types of balls. Explain what the notation means.
Consider the set of letters in the word "happy." Determine the best way to represent this set, and then write the set using either the roster method or set builder notation, whichever is more appropriate.
Write the cardinal value of each of the following sets in symbolic form.1. \(F=\{\) fork, spoon, knife, meat thermometer, can opener \(\}\)2. The empty set.
Classify each of the following sets as infinite or finite.1. \(E=\{2,4,6,8,10\}\)2. \(A\) is the set of lowercase letters of the English Alphabet, \(A=\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \ldots, \mathrm{z}\}\).3. \(\mathbb{Q}=\left\{\left.\frac{p}{q} \rightvert\, p\right.\) and \(q\) are integers
Determine if the following pairs of sets are equal, equivalent, or neither.1. \(E=\{2,4,6,8,10\}\) and \(F=\{\) fork, spoon, knife, meat thermometer, can opener \(\}\)2. The empty set and the set of prime numbers less than 2 .3. The set of vowels in the word happiness and the set of consonants in
Set \(L\) is a set of reading materials available in a shop at the airport, \(L=\{\) newspaper, magazine, book \(\}\). List all the subsets of set \(L\).
Consider the set of common political parties in the United States, \(P=\{\) Democratic, Green, Libertarian, Republican \(\}\). Determine if the following sets are proper subsets of \(P\).1. \(M=\{\) Democratic, Republican \(\}\)2. \(G=\{\) Green \(\}\)3. \(V=\{\) Republican, Libertarian, Green,
Consider the subsets of a standard deck of cards: \(S=\{\) spades, hearts, diamonds, clubs \(\} ; R=\{\) hearts, diamonds \(\}\); \(B=\{\) spades, clubs \(\} ;\) and \(C=\{\) clubs \(\}\).Express the relationship between the following sets symbolically.1. Set \(S\) and set \(B\).2. Set \(C\) and
Find the number of subsets of each of the following sets.1. The set of top five scorers of all time in the NBA:\(S=\{\) LeBron James, Kareem Abdul-Jabbar, Karl Malone, Kobe Bryant, Michael Jordan \(\}\).2. The set of the top four bestselling albums of all time:\(A=\{\) Thriller, Hotel California,
Using natural numbers, multiples of 3 are given by the sequence \(\{3,6,9, \ldots\}\). Write this set using set builder notation by expressing each multiple of 3 using a formula in terms of a natural number, \(n\).
A fast-food restaurant offers a deal where you can select two options from the following set of four menu items for \(\$ 6\) : a chicken sandwich, a fish sandwich, a cheeseburger, or 10 chicken nuggets. Javier and his friend Michael are each purchasing lunch using this deal. Create two equivalent,
A high school volleyball team at a small school consists of the following players: \{Angie, Brenda, Colleen, Estella, Maya, Maria, Penny, Shantelle\}. Create two possible equivalent starting line-ups of six players that the coach could select for the next game.
Write the relationship between the sets in the following Venn diagram, in words and symbolically. U= Dogs T = Terriers Figure 1.8
Describe the relationship between the sets in the following Venn diagram. U = 2D Figures T=Triangles S = Squares Figure 1.10
Draw a Venn diagram to represent the relationship between each of the sets.1. All rectangles are parallelograms.2. All women are people.
All bicycles and all cars have wheels, but no bicycle is a car. Draw a Venn diagram to represent this relationship.
For both of the questions below, \(A\) is a proper subset of \(U\).1. Given the universal set \(U=\{\) Billie Eilish, Donald Glover, Bruno Mars, Adele, Ed Sheeran \(\}\) and set \(A=\{\) Donald Glover, Bruno Mars, Ed Sheeran \(\}\), find \(A^{\prime}\).2. Given the universal set \(U=\{\mathrm{d}
Set \(A=\{1,3,5,7,9\}\) and \(B=\{2,3,5,7\}\). Find \(A\) intersection \(B\).
Set \(A=\{0,2,4,6,8\}\) and set \(B=\{1,3,5,7,9\}\). Find \(A \cap B\).
Set \(A=\{1,3,5, \ldots\}\) and set \(B=\mathbb{N}=\{1,2,3, \ldots\}\) Find \(A \cap B\).
Set \(A=\{1,3,5,7,9\}\) and set \(B=\{2,3,5,7\}\). Find \(A\) union \(B\).
Set \(A=\{0,2,4,6,8\}\) and set \(B=\{1,3,5,7,9\}\). Find \(A \cup B\).
Set \(A=\{1,3,5, \ldots\}\) and set \(B=\mathbb{N}=\{1,2,3, \ldots\}\). Find \(A \cup B\).
The number of elements in set \(A\) is 10 , the number of elements in set \(B\) is 20 , and the number of elements in \(A\) intersection \(B\) is 4 . Find the number of elements in \(A\) union \(B\).
If \(A\) and \(B\) are disjoint sets and the cardinality of set \(A\) is 37 and the cardinality of set \(B\) is 43 , find the cardinality of \(A\) union \(B\).
\(A=\{0,3,6,9,12\}, B=\{0,4,8,12,16\}\), and \(C=\{1,2,3,5,8,13\}\).Find the set consisting of elements in:1. \(A\) and \(B\).2. \(A\) or \(B\).3. \(A\) or \(C\).4. \((B\) and \(C)\) or \(A\).
Don Woods is serving cake and ice cream at his Juneteenth celebration. The party has a total of 54 guests in attendance. Suppose 30 guests requested cake, 20 guests asked for ice cream, and 12 guests did not have either cake or ice cream.1. How many guests had cake or ice cream?2. How many guests
1. Find \(A \cup B\).2. Find \(A \cap B\).3. Find \(B^{\prime}\).4. Find \(n\left(B^{\prime}\right)\). U {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} A 1 B 3 5 7 6 8 9 0 Figure 1.26
1. Find \(n(A\) or \(B)\).2. Find \(n(A\) and \(B)\).3. Find \(n(A)\). U A 5 2 B 8 00
Use the Venn diagram below, which shows the blood types of 100 people who donated blood at a local clinic, to answer the following questions.1. How many people with a type \(A\) blood factor donated blood?2. Julio has blood type \(\mathbf{B}^{+}\). If he needs to have surgery that requires a blood
A teacher surveyed her class of 43 students to find out how they prepared for their last test. She found that 24 students made flash cards, 14 studied their notes, and 27 completed the review assignment. Of the entire class of 43 students, 12 completed the review and made flash cards, nine
Perform the set operations as indicated on the following sets: \(U=\{0,1,2,3,4,5,6,7,8,9,10,11,12\}\), \(A=\{0,1,2,3,4,5,6\}, B=\{0,2,4,6,8,10,12\}\), and \(C=\{0,3,6,9,12\}\).1. Find \((A \cap B) \cap C\).2. Find \(A \cap(B \cup C)\).3. Find \((A \cap B) \cup C^{\prime}\)
De Morgan's Law for the complement of the union of two sets \(A\) and \(B\) states that: \((A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}\). Use a Venn diagram to prove that De Morgan's Law is true.
The set of primary colors: red, yellow, and blue.For the following exercises, represent each set using the roster method.
A set of the following flowers: rose, tulip, marigold, iris, and lily.For the following exercises, represent each set using the roster method.
The set of natural numbers between 50 and 100 .For the following exercises, represent each set using the roster method.
The set of natural numbers greater than 17 .For the following exercises, represent each set using the roster method.
The set of different pieces in a game of chess.For the following exercises, represent each set using the roster method.
The set of natural numbers less than 21.For the following exercises, represent each set using the roster method.
The set of all types of lizards.For the following exercises, represent each set using set builder notation.
The set of all stars in the universe.For the following exercises, represent each set using set builder notation.
The set of all integer multiples of 3 that are greater than zero.For the following exercises, represent each set using set builder notation.
The set of all integer multiples of 4 that are greater than zero.For the following exercises, represent each set using set builder notation.
The set of all plants that are edible.For the following exercises, represent each set using set builder notation.
The set of all even numbers.For the following exercises, represent each set using set builder notation.
The set of all squares that are also circles.For the following exercises, represent each set using the method of your choice.
The set of natural numbers divisible by zero.For the following exercises, represent each set using the method of your choice.
The set of Mike and Carol's children on the TV show, The Brady Bunch.For the following exercises, represent each set using the method of your choice.
The set of all real numbers.For the following exercises, represent each set using the method of your choice.
The set of polar bears that live in Antarctica.For the following exercises, represent each set using the method of your choice.
The set of songs written by Prince.For the following exercises, represent each set using the method of your choice.
The set of children's books written and illustrated by Mo Willems.For the following exercises, represent each set using the method of your choice.
The set of seven colors commonly listed in a rainbow.For the following exercises, represent each set using the method of your choice.
The names of all the characters in the book. The Fault in Our Stars by John Green.For the following exercises, determine if the collection of objects represents a well-defined set or not.
The five greatest soccer players of all time.For the following exercises, determine if the collection of objects represents a well-defined set or not.
A group of old dogs that are able to learn new tricks.For the following exercises, determine if the collection of objects represents a well-defined set or not.
A list of all the movies directed by Spike Lee as of 2021.For the following exercises, determine if the collection of objects represents a well-defined set or not.
The group of all zebras that can fly an airplane.For the following exercises, determine if the collection of objects represents a well-defined set or not.
The group of National Baseball League Hall of Fame members who have hit over 700 career home runs.For the following exercises, determine if the collection of objects represents a well-defined set or not.
\(P=\{\) Snuzzle, Butterscotch, Blue Belle, Minty, Blossom, Cotton Candy \(\}\)For the following exercises, compute the cardinal value of each set.
\(T=\{\) pepperoni, sausage, bacon, ham, mushrooms, olives, bell pepper, pineapple \(\}\)For the following exercises, compute the cardinal value of each set.
\(\varnothing\)For the following exercises, compute the cardinal value of each set.
\(B=\{5,6,7, \ldots, 20\}\)For the following exercises, compute the cardinal value of each set.
\(F=\left\{\frac{1}{9}, \frac{2}{9}, \frac{3}{9}, \frac{4}{9}, \frac{5}{9}, \frac{6}{9}, \frac{7}{9}, \frac{8}{9}, \frac{9}{9}\right\}\)For the following exercises, compute the cardinal value of each set.
{ }For the following exercises, compute the cardinal value of each set.
\(C=\left\{n^{3} \mid n\right.\) is a member of \(\left.\mathbb{N}\right\}\)For the following exercises, compute the cardinal value of each set.
\(S=\{7 n \mid n\) is an element of \(\mathbb{N}\}\)For the following exercises, compute the cardinal value of each set.
\(L=\{l, m, n, \ldots, y\}\)For the following exercises, compute the cardinal value of each set.
The set of numbers on a standard 6 -sided die.For the following exercises, compute the cardinal value of each set.
\(A=\{\) right, acute, obtuse \(\} ; B=\{\) equilateral, scalene, isoceles \(\}\).For the following exercises, determine whether set \(A\) and set \(B\) are equal, equivalent or neither.
\(A=\left\{1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}\right\} ; B=\left\{\frac{1}{4}, \frac{1}{3}, \frac{1}{2}, 1\right\}\).For the following exercises, determine whether set \(A\) and set \(B\) are equal, equivalent or neither.
\(A=\{\) red, orange, yellow \(\} ; B=\{\) green, blue, indigo, violet \(\}\).For the following exercises, determine whether set \(A\) and set \(B\) are equal, equivalent or neither.
\(A=\{5 n \mid n \in \mathbb{N}\} ; B=\mathbb{N}\).For the following exercises, determine whether set \(A\) and set \(B\) are equal, equivalent or neither.
\(A=\{-2,-1,0, \ldots\} ; B=\{2,3,5, \ldots\}\).For the following exercises, determine whether set \(A\) and set \(B\) are equal, equivalent or neither.
\(A=\{\) John, Paul, George, Ringo \(\} ; B=\{\) Bono, Larry, The Edge, Adam \(\}\).For the following exercises, determine whether set \(A\) and set \(B\) are equal, equivalent or neither.
\(A=\varnothing ; B=\{\}\).For the following exercises, determine whether set \(A\) and set \(B\) are equal, equivalent or neither.
\(A=\{\) lemon, lime, orange \(\} ; B=\{\) orange, lemon, lime, grape \(\}\).For the following exercises, determine whether set \(A\) and set \(B\) are equal, equivalent or neither.
The set of natural numbers.For the following exercises, determine if the set described is finite or infinite.
The empty set.For the following exercises, determine if the set described is finite or infinite.
The set consisting of all jazz venues in New Orleans, Louisiana.For the following exercises, determine if the set described is finite or infinite.
The set of all real numbers.For the following exercises, determine if the set described is finite or infinite.
The set of all different types of cheeses.For the following exercises, determine if the set described is finite or infinite.
The set of all words in Merriam-Webster's Collegiate Dictionary, Eleventh Edition, published in 2020.For the following exercises, determine if the set described is finite or infinite.
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