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mathematics
contemporary mathematics

Contemporary Mathematics 1st Edition OpenStax - Solutions

In English, a conjunction is a word that connects two phrases or parts of a sentence together.Determine whether the sentence represents a logical statement. If it is a logical statement, determine whether it is true or false.
\(8-3=5\).Determine whether the sentence represents a logical statement. If it is a logical statement, determine whether it is true or false.
\(7+3=11\).Determine whether the sentence represents a logical statement. If it is a logical statement, determine whether it is true or false.
What is 7 plus 3 ?Determine whether the sentence represents a logical statement. If it is a logical statement, determine whether it is true or false.
Grammy award winning singer, Lady Gaga, was not born in Houston, Texas.Write each statement in symbolic form.
Bruno Mars performed during the Super Bowl halftime show twice.Write each statement in symbolic form.
Coco Chanel said, "The most courageous act is still to think for yourself. Aloud."Write each statement in symbolic form.
Bruce Wayne is not Superman.Write each statement in symbolic form.
Bozo is not a clown.Write the negation of each statement in words.
Ash is Pikachu's trainer and friend.Write the negation of each statement in words.
Vanilla is the most popular flavor of ice cream.Write the negation of each statement in words.
Smaug is a fire breathing dragon.Write the negation of each statement in words.
Elephant and Piggy are not best friends.Write the negation of each statement in words.
Some dogs like cats.Write the negation of each statement in words.
Some donuts are not round.Write the negation of each statement in words.
All cars have wheels.Write the negation of each statement in words.
No circles are squares.Write the negation of each statement in words.
Nature's first green is not gold.Write the negation of each statement in words.
The ancient Greek philosopher Plato said, "The greatest wealth is to live content with little."Write the negation of each statement in words.
All trees produce nuts.Write the negation of each statement in words.
\(p\) : Their hair is red.Write the negation of each statement symbolically and in words.
\(\sim q\) : My favorite superhero does not wear a cape.Write the negation of each statement symbolically and in words.
\(s\) : All wolves howl at the moon.Write the negation of each statement symbolically and in words.
\(t\) : Nobody messes with Texas.Write the negation of each statement symbolically and in words.
\(\sim\) u: I do not love New York.Write the negation of each statement symbolically and in words.
\(\sim v\) : Some cats are not tigers.Write the negation of each statement symbolically and in words.
\(\sim q\) : No squares are not parallelograms.Write the negation of each statement symbolically and in words.
\(\sim p\) : The President does not like broccoli.Write the negation of each statement symbolically and in words.
Given: \(p\) : Kermit is a green frog; translate \(\sim p\) into words.Write each of the following symbolic statements in words.
Given: \(\sim r\) : Mick Jagger is not the lead singer for The Rolling Stones; translate \(r\) into words.Write each of the following symbolic statements in words.
Given: \(q\) : All dogs go to heaven; translate \(\sim q\) into words.Write each of the following symbolic statements in words.
Given: \(\sim s\) : Some pizza does not come with pepperoni on it; translate \(s\) into words.Write each of the following symbolic statements in words.
Given: \(\sim\) : No pizza comes with pineapple on it; translate \(\sim(\sim p)\) into words.Write each of the following symbolic statements in words.
Given: \(r\) : Not all roses are red; translate \(\sim(\sim r)\) into words.Write each of the following symbolic statements in words.
Given: \(\sim t\) : Thelonious Monk is not a famous jazz pianist; translate \(\sim(\sim t)\) into words.Write each of the following symbolic statements in words.
Given: \(\sim v\) : Not all violets are blue; translate \(\sim(\sim v)\) into words.Write each of the following symbolic statements in words.
The Ford Motor Company builds cars in Michigan. General Motors builds cars in Michigan. Chrysler builds cars in Michigan. What conclusion can be drawn from these premises?Draw a logical conclusion from the premises that includes one of the following quantifiers: all, some, or none.
Michelangelo Buonarroti was a great Renaissance artist from Italy. Raphael Sanzio was a great Renaissance artist from Italy. Sandro Botticelli was a great Renaissance artist from Italy. What conclusion can you draw from these premises?Draw a logical conclusion from the premises that includes one of
Four is an even number and it is divisible by 2 . Six is an even number and it is divisible by 2 . Eight is an even number and it is divisible by 2 . What conclusion can you draw from these premises?Draw a logical conclusion from the premises that includes one of the following quantifiers: all,
Three is an odd number and it is not divisible by 2 . Seven is an odd number and it is not divisible by 2 . Twenty one is an odd number and it is not divisible by 2 . What conclusion can you draw from these premises?Draw a logical conclusion from the premises that includes one of the following
The odd number 5 is not divisible by 3 . The odd number 7 is not divisible by 3 . The odd number 29 is not divisible by 3 . What conclusion can you draw from these premises?Draw a logical conclusion from the premises that includes one of the following quantifiers: all, some, or none.
Penguins are flightless birds. Emus are flightless birds. Ostriches are flightless birds. What conclusion can you draw from these premises?Draw a logical conclusion from the premises that includes one of the following quantifiers: all, some, or none.
Plants need water to survive. Animals need water to survive. Bacteria need water to survive. What conclusion can you draw from these premises?Draw a logical conclusion from the premises that includes one of the following quantifiers: all, some, or none.
A chocolate chip cookie is not sour. An oatmeal cookie is not sour. An Oreo cookie is not sour. What conclusion can you draw from these premises?Draw a logical conclusion from the premises that includes one of the following quantifiers: all, some, or none.
Determine whether each of the following sentences represents a logical statement. If it is a logical statement, determine whether it is true or false.1. Tiger Woods won the Master's golf championship at least five times.2. Please, sit down over there.3. All cats dislike dogs.
Write each of the following logical statements in symbolic form.1. Barry Bonds holds the Major League Baseball record for total career home runs.2. Some mammals live in the ocean.3. Ruth Bader Ginsburg served on the U.S. Supreme Court from 1993 to 2020.
Write the negation of each logical statement in words.1. Michael Phelps was an Olympic swimmer.2. Tom is a cat.3. Jerry is not a mouse.
Write the negation of each logical statement symbolically.1. \(p\) : Michael Phelps was an Olympic swimmer.2. \(r\) : Tom is not a cat.3. \(\sim q\) : Jerry is not a mouse.
Given the statements:\(r\) : Elmo is a red Muppet.\(p\) : Ketchup is not a vegetable.1. Write the symbolic form of the statement, "Elmo is not a red Muppet."2. Translate the statement \(\sim p\) into words.
For each series of premises, draw a logical conclusion to the argument that includes one of the following quantifiers: all, some, or none.1. Squares and rectangles have four sides. A square is a parallelogram, and a rectangle is a parallelogram. What conclusion can be drawn from these premises?2.
Given the statements:p: All leopards have spots.\(r\) : Some apples are red.\(s\) : No lemons are sweet.Write each of the following symbolic statements in words.1. \(\sim p\)2. \(\sim r\)3. \(\sim S\)
For each of the following connectives, write its name and associated symbol.1. or 2. implies 3. but
Let \(p\) represent the statement, "It is a warm sunny day," and let \(q\) represent the statement, "the family will go to the beach." Write the symbolic form of each of the following compound statements.1. If it is a warm sunny day, then the family will go to the beach.2. The family will go to the
Let \(p\) represent the statement, "My child finished their homework," let \(q\) represent the statement, "My child cleaned her room," let \(r\) represent the statement, "My child played video games," and let \(s\) represent the statement, "My child streamed a movie." Translate each of the
For each of the following compound logical statements, add parentheses to indicate the order to evaluate the statement. Recall that parentheses are evaluated innermost first.1. \(p \wedge \sim q \vee r\)2. \(q \rightarrow \sim p \wedge r\)3. \(\sim(p \vee q) \leftrightarrow \sim p \wedge \sim q\)
For each logical statement, determine the truth value of its negation.1. \(p: 3+5=8\).2. \(q\) : All horses are mustangs.3. \(\sim r\) : New Delhi is not the capital of India.
Given \(p: 4+7=11, q: 11-3=7\), and \(r: 7 \times 11=77\), determine the truth value of each conjunction.1. \(p \wedge q\)2. \(\sim q \wedge r\)3. \(\sim p \wedge q\)
Given \(p: 4+7=11, q: 11- 3=7\), and \(r: 7 \times 11=77\), determine the truth value of each disjunction.1. \(p \vee q\)2. \(\sim q \vee r\)3. \(\sim p \vee q\)
Given \(p: 4+7=11, q: 11-3=7\), and \(r: 7 \times 11=77\), construct a truth table to determine the truth value of each compound statement 1. \(\sim p \wedge q \vee r\)2. \(\sim p \vee q \wedge r\)3. \(\sim(p \wedge r) \vee q\)
Construct a truth table to analyze all possible outcomes for each of the following arguments.1. \(p \vee \sim q\)2. \(\sim(p \wedge q)\)3. \((p \vee \sim q) \wedge r\)
Construct a truth table to determine the validity of each of the following statements.1. \(\sim p \wedge q\)2. \(\sim(p \wedge \sim p)\)
Assume both of the following statements are true: \(p\) : My sibling washed the dishes, and \(q\) : My parents paid them \(\$ 5.00\). Create a truth table to determine the truth value of each of the following conditional statements.1. \(p \rightarrow q\)2. \(p \rightarrow \sim q\)3. \(\sim p
Construct a truth table to analyze all possible outcomes for each of the following statements then determine whether they are valid.1. \(p \wedge q \rightarrow \sim q\)2. \(p \rightarrow \sim p \vee q\)
Assume both of the following statements are true: \(p\) : The plumber fixed the leak, and \(q\) : The homeowner paid the plumber \(\$ 150.00\). Create a truth table to determine the truth value of each of the following biconditional statements.1. \(p \leftrightarrow q\)2. \(p \leftrightarrow \sim
Construct a truth table to analyze all possible outcomes for each of the following statements, then determine whether they are valid.1. \(p \wedge q \leftrightarrow p \wedge \sim q\)2. \(p \vee q \leftrightarrow \sim p \vee q\)3. \(p \rightarrow q \leftrightarrow \sim q \rightarrow \sim p\)4. \(p
Create a truth table to determine whether the following compound statements are logically equivalent.1. \(p \rightarrow q ; \sim p \rightarrow \sim q\)2. \(p \rightarrow q ; \sim p \vee q\)
Use the statements, \(p\) : Harry is a wizard and \(q\) : Hermione is a witch, to write the following statements:1. Write the conditional statement, \(p \rightarrow q\), in words.2. Write the converse statement, \(q \rightarrow p\), in words.3. Write the inverse statement, \(\sim p \rightarrow \sim
Use the conditional statement, "If all dogs bark, then Lassie likes to bark," to identify the following.1. Write the hypothesis of the conditional statement and label it with a \(p\).2. Write the conclusion of the conditional statement and label it with a \(q\).3. Identify the following statement
Assume the conditional statement, \(p \rightarrow q\) : "If Chadwick Boseman was an actor, then Chadwick Boseman did not star in the movie Black Panther" is false, and use it to answer the following questions.1. Write the converse of the statement in words and determine its truth value.2. Write the
Write the negation of each statement in words without using the phrase, "It is not the case that."1. Kristin is a biomedical engineer and Thomas is a chemical engineer.2. A person had cake or they had ice cream.
Write the negation of each conditional statement.1. If Adele won a Grammy, then she is a singer.2. If Henrik Lundqvist played professional hockey, then he did not win the Stanley Cup.
Write the negation of each conditional statement.1. If all cats purr, then my partner's cat purrs.2. If a penguin is a bird, then some birds do not fly.
Write the negation of each conditional statement applying De Morgan's Law.1. If mom needs to buy chips, then Mike had friends over and Bob was hungry.2. If Juan had pizza or Chris had wings, then dad watched the game.
Construct a truth table to verify De Morgan's Law for the negation of a conjunction, \(\sim(p \wedge q) \equiv \sim p \vee \sim q\), is valid.
Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of detachment to determine a valid conclusion.1. If Leonardo da Vinci was an artist, then he painted the Mona Lisa. Leonardo da Vinci was an artist.2. If Michael Jordan played for the
Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of denying the consequent to determine a valid conclusion.1. If Leonardo da Vinci was an artist, then he painted the Mona Lisa. Leonardo da Vinci did not paint the Mona Lisa.2. If Michael
Each pair of statements represents true premises in a logical argument. Based on these premises, apply the chain rule for conditional arguments to determine a valid and sound conclusion.1. If my roommate goes to work, then my roommate will get paid. If my roommate gets paid, then my roommate will
Write a set consisting of four small hand tools that might be in a toolbox and label it with a capital \(T\).
For each of the following collections, determine if it represents a well-defined set.1. A collection of medium-sized potatoes.2. The original members of the Black Eyed Peas musical group.
Represent the set of all numbers divisible by 0 symbolically.
Use an ellipsis to write the set of single digit numbers greater than or equal to zero and label it with a capital \(D\).
Write the set of odd numbers greater than 0 and label it with a capital \(M\).
Using set builder notation, write the set \(C\) of all types of cars.
Use the roster method or set builder notation to represent the collection of all musical instruments.
Write the cardinal value of each of the following sets in symbolic form.1. Set \(P\) is the set of prime numbers less than 2 .2. Set \(A\) is the set of lowercase letters of the English alphabet, \(A=\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \ldots, \mathrm{z}\}\).
Classify each of the following sets as infinite or finite.1. \(B=\{b, a, k, e\}\)2. \(\mathbb{R}=\{x \mid x\) is a real number \(\}\)
Determine if the following pairs of sets are equal, equivalent, or neither.1. Set \(B=\{b, a, k, e\}\) and set \(A=\{a, b, e, k\}\)2. Set \(B=\{b, a, k, e\}\) and set \(F=\{f, l, a, k, e\}\)3. Set \(B=\{b, a, k, e\}\) and set \(C=\{c, a, k, e\}\)
Consider the set of possible outcomes when you flip a coin, \(S=\{\) heads, tails \(\}\). List all the possible subsets of set \(S\).
Consider the set of generation I legendary Pokémon, \(L=\{\) Articuno, Zapdos, Moltres, Mewtwo \(\}\). Give an example of a proper subset containing:1. one member.2. three members.3. no members.
Express the relationship between the set of natural numbers, \(\mathbb{N}=\{1,2,3, \ldots\}\), and the set of even numbers, \(E=\{2,4,6, \ldots\}\).
Compute the total number of subsets in the set of the top nine tennis grand slam singles winners, \(T=\{\) Margaret Court, Serena Williams, Steffi Graff, Rafael Nadal, Novak Djokovic, Roger Federer, Helen Wills, Martina Navratilova, Chris Everett \(\}.\)
Using natural numbers, multiples of 5 are given by the sequence \(\{5,10,15, \ldots\}\). Write this set using set builder notation by associating each multiple of 5 in terms of a natural number, \(n\).
Serena and Venus Williams walk into the same restaurant as Javier and Michael, but they order the same pair of items, resulting in equal sets of choices. If Venus ordered a fish sandwich and chicken nuggets, what did Serena order?
Consider the same group of volleyball players from above: \{Angie, Brenda, Colleen, Estella, Maya, Maria, Penny, Shantelle\}. The team needs to select a captain and an assistant captain from their members. List two possible equivalent subsets that they could select.
1. Draw a Venn diagram to represent the relationship between each of the sets. All natural numbers are integers.2. \(A \subset U\). Draw a Venn diagram to represent this relationship.
Airplanes and birds can fly, but no birds are airplanes. 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 \(U=\{\) red, orange, yellow, green, blue, indigo, violet \(\}\) and set \(A=\{\) yellow, red, blue \(\}\), find \(A^{\prime}\).2. Given the universal set \(U=\{c \mid c\) is a cat \(\}\) and set \(A=\{c
Set \(A=\{h, a, p, y\}\) and \(B=\{s, a, d\}\). Find \(A\) intersection \(B\).
Set \(A=\{\) red, yellow, blue \(\}\) and set \(B=\{\) orange, green, purple \(\}\). Find \(A \cap B\).
Set \(A=\{a, b, c, \ldots, z\}\) and set \(B=\{a, e, i, o, u\}\). Find \(A \cap B\).

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