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mathematics
contemporary mathematics
Contemporary Mathematics 1st Edition OpenStax - Solutions
\(p \vee q \leftrightarrow r\)Given: \(p\) : Frodo is a hobbit, \(q\) : Gandalf is a wizard, \(r\) : Frodo and Samwise will take the ring to Mordor, and \(s\) : Gollum will help Frodo get into Mordor.Translate the symbolic form of each compound logical statement into words.
\(\sim(\sim r \vee \sim s)\)Given: \(p\) : Frodo is a hobbit, \(q\) : Gandalf is a wizard, \(r\) : Frodo and Samwise will take the ring to Mordor, and \(s\) : Gollum will help Frodo get into Mordor.Translate the symbolic form of each compound logical statement into words.
Frodo and Samwise will take the ring to Mordor or Gandalf is not a wizard and Frodo is a hobbit.Translate the written form of each compound logical statement into symbolic form.
If Gollum will not help Frodo get into Mordor, then Gandalf is not a wizard and Frodo is not a hobbit.Translate the written form of each compound logical statement into symbolic form.
\(\sim p \rightarrow q \leftrightarrow r\)For each of the following compound logical statement, apply the proper dominance of connectives by adding parentheses to indicate the order in which the statement must be evaluated.
\(\sim(p \wedge q) \leftrightarrow \sim p \vee \sim q\)For each of the following compound logical statement, apply the proper dominance of connectives by adding parentheses to indicate the order in which the statement must be evaluated.
Complete the truth table to determine the truth value of the proposition in the last column. 14 (b~d) (bvd) b~ Ad b- byd b d
If a triangle is a right triangle, then it does not have one 90 -degree angle or \(a^{2}+b^{2}=c^{2}\).Given the true statements p: "A right triangle has one 90 -degree angle," \(q\) : "The triangle is a right triangle," \(r\) : " \(a^{2}+b^{2}=c^{2}\)," and \(s\) : "The longest side of a triangle
The triangle is a right triangle, or a right triangle does not have a 90 -degree angle, if and only if it is not the case that the longest side of a triangle is \(c\) implies \(a+b\) must be \(>c\).Given the true statements p: "A right triangle has one 90 -degree angle," \(q\) : "The triangle is a
Write the converse statement in words.Use the conditional statement, \(p \rightarrow q\) : "If Phil Mickelson is 50 years old, then Phil Mickelson won the Player's Championship," to answer the following questions.
If the conditional statement is true, and the hypothesis is true, what is a valid conclusion to the argument?Use the conditional statement, \(p \rightarrow q\) : "If Phil Mickelson is 50 years old, then Phil Mickelson won the Player's Championship," to answer the following questions.
If the conditional statement is true, and the conclusion is false, what is a valid conclusion to the argument?Use the conditional statement, \(p \rightarrow q\) : "If Phil Mickelson is 50 years old, then Phil Mickelson won the Player's Championship," to answer the following questions.
Construct a truth table to analyze all the possible outcomes and determine the validity of the following argument. \(\sim p \vee q \leftrightarrow q \rightarrow p\)
Construct a truth table or Venn diagram to prove whether the following argument is valid. If the argument is valid, determine whether it is sound.If John Mayer played MTV unplugged, then some guitars are acoustic. John Mayer played MTV unplugged. Therefore, some guitars are acoustic.
24 Use divisibility rules to determine if each of the following is divisible by 2 .
37 Use divisibility rules to determine if each of the following is divisible by 2 .
\(1,345,321\)Use divisibility rules to determine if each of the following is divisible by 2 .
48 Use divisibility rules to determine if each of the following is divisible by 3.
210 Use divisibility rules to determine if each of the following is divisible by 3.
\(5,345,324\)Use divisibility rules to determine if each of the following is divisible by 3.
130 Use divisibility rules to determine if each of the following is divisible by 5 .
237 Use divisibility rules to determine if each of the following is divisible by 5 .
\(1,345,321\)Use divisibility rules to determine if each of the following is divisible by 5 .
48 Use divisibility rules to determine if each of the following is divisible by 9 .
210 Use divisibility rules to determine if each of the following is divisible by 9 .
\(5,345,325\)Use divisibility rules to determine if each of the following is divisible by 9 .
48 Use divisibility rules to determine if each of the following is divisible by 12 .
210 Use divisibility rules to determine if each of the following is divisible by 12 .
\(5,355,324\)Use divisibility rules to determine if each of the following is divisible by 12 .
Determine which of the following numbers are prime: \(\{3,27,77,131,457\}\)
Determine which of the following numbers are prime: \(\{31,97,188,389\}\)
12 Find the prime factorization of the given number.
53 Find the prime factorization of the given number.
72 Find the prime factorization of the given number.
345 Find the prime factorization of the given number.
938 Find the prime factorization of the given number.
36,068 Find the prime factorization of the given number.
\(8,211,679\)Find the prime factorization of the given number.
\(\{45,245\}\)Find the greatest common divisor of the given set of numbers.
\(\{11,24\}\)Find the greatest common divisor of the given set of numbers.
\(\{56,44\}\)Find the greatest common divisor of the given set of numbers.
\(\{150,600\}\)Find the greatest common divisor of the given set of numbers.
\(\{1,746,28,324\}\)Find the greatest common divisor of the given set of numbers.
\(\{30,40,75\}\)Find the greatest common divisor of the given set of numbers.
\(\{19,45,70\}\)Find the greatest common divisor of the given set of numbers.
\(\{293,7,298,19,229\}\)Find the greatest common divisor of the given set of numbers.
\(\{3,927,473,82,709,1,210,121\}\)Find the greatest common divisor of the given set of numbers.
Make a list of the common divisors of 12 and 18 . What is the GCD of 12 and 18 ? Which of the other common divisors of 12 and 18 divide the GCD?
Make a list of the common divisors of 20 and 84 . What is the GCD? Which of the other common divisors of 20 and 84 also divide the GCD?
Make a list of the common divisors of 120 and 88.What is the GCD? Which of the other common divisors of 120 and 88 also divide the GCD?
Based on the answers to 34,35 , and 36 , make a conjecture about the GCD of two numbers, and the other common divisors of those numbers.
Rebecca wants to cut two lengths of board into equal length pieces, with no leftover piece. The two boards are \(230 \mathrm{~cm}\) long and \(370 \mathrm{~cm}\) long. What is the longest length that Rebecca can cut from these boards so that all the cut boards are the same length?
Yasmin is playing with her younger brother, Cameron. They are grouping Skittles by color. They have 14 green, 10 yellow, and 8 purple Skittles. Each group must have the same number of green, the same number of yellow, and the same number of purple Skittles. What's the maximum number of piles that
Gathii is creating a tile backsplash for his kitchen. He wants to use square tiles to cover a \(330 \mathrm{~cm} \times 12 \mathrm{~cm}\) area. What is the largest size square tile he can use to create this backsplash?
Deiji is designing a contest where teams will be given the same number of toothpicks, \(5 \mathrm{oz}\). paper cups, and 2 cm length pieces of string. She has 420 pieces of string, 300 paper cups, and 1,610 toothpicks. What is the maximum number of teams she can have so that every team gets an
\(\{30,40\}\)Find the least common multiple of the given set of numbers.
\(\{11,24\}\)Find the least common multiple of the given set of numbers.
\(\{14,45\}\)Find the least common multiple of the given set of numbers.
\(\{200,450\}\)Find the least common multiple of the given set of numbers.
\(\{38,077,9,088,687\}\)Find the least common multiple of the given set of numbers.
\(\{36,42,70\}\)Find the least common multiple of the given set of numbers.
\(\{7,13,36\}\)Find the least common multiple of the given set of numbers.
\(\{4,450,864,339,889,157,339\}\)Find the least common multiple of the given set of numbers.
Benjamin and Mia both work at the Grease Fire diner, a local eatery. Benjamin has every 4th day off, and Mia has every 6th day off. How many days pass until they have another day off together?
A lunar month is 30 days (rounding off). A new lunar month begins on a Saturday. How many days is it until a lunar month begins on a Saturday again?
Isabella is creating a collage for a project and wants a horizontal cut in the collage. The cut will be made by using purple strips of cloth that are \(28 \mathrm{~mm}\) long, and yellow strips of paper that are \(36 \mathrm{~mm}\) long. What is the minimum length of the cut can she make using
Asteroids are objects that orbit the sun. The smallest distance that an asteroid gets to the sun during its orbit is called the perihelion. Asteroids also have orbital periods, or the time it takes to go around the sun exactly one time. The asteroid Ceres has an orbital period (number of days to
If Apple Inc. releases a new iPhone, then customers will buy it. Customers did not buy a new iPhone. Therefore, Apple Inc. did not release a new iPhone.Analyze the argument and identify the form of the argument as the law of detachment, the law of denying the consequent, the chain rule for
In the animated movie Toy Story, if Paul Newman turned down the role of voicing Woody, then Tom Hanks was chosen for the role. Tom Hanks was chosen as the voice for Woody, therefore, Paul Newman turned down the role of voicing Woody in Toy Story.Analyze the argument and identify the form of the
\(p \rightarrow q\) and \(q \rightarrow r . \therefore p \rightarrow r\).Analyze the argument and identify the form of the argument as the law of detachment, the law of denying the consequent, the chain rule for conditional arguments, or none of these.
\(p \rightarrow q\) and \(p . \therefore q\).Analyze the argument and identify the form of the argument as the law of detachment, the law of denying the consequent, the chain rule for conditional arguments, or none of these.
\(p \rightarrow q\) and \(\sim q . \therefore \sim p\).Analyze the argument and identify the form of the argument as the law of detachment, the law of denying the consequent, the chain rule for conditional arguments, or none of these.
If all people are created equal, then all people are the same with respect to the law. If all people are the same with respect to the law, then justice is blind. Therefore, if all people are created equal, then justice is blind.Analyze the argument and identify the form of the argument as the law
If I mow the lawn, then my caregiver will pay me twenty dollars. I mowed the lawn. Therefore, my caregiver paid me twenty dollars.Analyze the argument and identify the form of the argument as the law of detachment, the law of denying the consequent, the chain rule for conditional arguments, or none
If Robin Williams was a comedian, then some comedians are funny. No comedians are funny. Therefore, Robin Williams was not a comedian.Analyze the argument and identify the form of the argument as the law of detachment, the law of denying the consequent, the chain rule for conditional arguments, or
\(p \rightarrow \sim q\) and \(p\).Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of detachment to determine and write a valid conclusion.
\(\sim p \rightarrow q\) and \(\sim p\).Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of detachment to determine and write a valid conclusion.
If Richard Harris played Dumbledore, then Daniel Radcliffe played Harry Potter. Richard Harris played Dumbledore.Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of detachment to determine and write a valid conclusion.
If Emma Watson is an actor, then Emma Watson starred as Belle in the movie Beauty and the Beast. Emma Watson is an actor.Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of detachment to determine and write a valid conclusion.
If some Granny Smiths are available, then we will make an apple pie. Some Granny Smiths are available.Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of detachment to determine and write a valid conclusion.
If Peter Rabbit lost his coat, then all rabbits must avoid Mr. McGregor's garden. Peter Rabbit lost his coat.Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of detachment to determine and write a valid conclusion.
If Greg and Ralph are friends, then Greg will not play a prank on Ralph. Greg played a prank on Ralph.Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of denying the consequent to determine and write a valid conclusion.
If Drogon is not a dragon, then Daenerys ruled Westeros. Daenerys did not rule Westeros.Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of denying the consequent to determine and write a valid conclusion.
\(p \rightarrow \sim q\) and \(q\).Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of denying the consequent to determine and write a valid conclusion.
\(\sim p \rightarrow q\) and \(\sim q\).Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of denying the consequent to determine and write a valid conclusion.
If all dragons breathe fire, then rainwings are not dragons. Rainwings are dragons.Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of denying the consequent to determine and write a valid conclusion.
If some pirates have parrots as pets, then some parrots do not like crackers. All parrots like crackers.Each pair of statements represents the premises in a logical argument. Based on these premises, apply the law of denying the consequent to determine and write a valid conclusion.
\(\sim p \rightarrow q\) and \(q \rightarrow \sim r\).Each pair of statements represent true premises in a logical argument. Based on these premises, apply the chain rule for conditional arguments to determine a valid and sound conclusion.
\(r \rightarrow \sim q\) and \(\sim q \rightarrow \sim p\).Each pair of statements represent true premises in a logical argument. Based on these premises, apply the chain rule for conditional arguments to determine a valid and sound conclusion.
\(q \rightarrow r\) and \(p \rightarrow q\).Each pair of statements represent true premises in a logical argument. Based on these premises, apply the chain rule for conditional arguments to determine a valid and sound conclusion.
\(\sim r \rightarrow p\) and \(q \rightarrow \sim r\).Each pair of statements represent true premises in a logical argument. Based on these premises, apply the chain rule for conditional arguments to determine a valid and sound conclusion.
If Mr. Spock is a science officer, then Montgomery Scott is an engineer. If Montgomery Scott is an engineer, then James T. Kirk is the captain.Each pair of statements represent true premises in a logical argument. Based on these premises, apply the chain rule for conditional arguments to determine
If Prince Charles is a character from Star Wars, then Luke Skywalker is not a Jedi. If Luke Skywalker is not a Jedi, then Darth Vader is not his father.Each pair of statements represent true premises in a logical argument. Based on these premises, apply the chain rule for conditional arguments to
If my siblings drink milk out of the carton, then they will leave the carton on the counter. My siblings did not leave the carton on the counter.Each pair of statements represent true premises in a logical argument. Based on these premises, state a valid conclusion based on the form of the argument.
If my friend likes to bowl, then my partner does not like to play softball. My friend likes to bowl.Each pair of statements represent true premises in a logical argument. Based on these premises, state a valid conclusion based on the form of the argument.
If mathematics is fun, then students will study algebra. If students study algebra, then they will score a 100 on their final exam.Each pair of statements represent true premises in a logical argument. Based on these premises, state a valid conclusion based on the form of the argument.
If all fleas bite and our dog has fleas, then our dog will scratch a lot. Our dog will not scratch a scratch a lot.Each pair of statements represent true premises in a logical argument. Based on these premises, state a valid conclusion based on the form of the argument.
If the toddler is not tall, then they will use a stepladder to reach the cookie jar. If the toddler will use a stepladder to reach the cookie jar, then they will drop the jar. If they drop the cookie jar, then they will not eat any cookies.Each pair of statements represent true premises in a
If you do not like to dance, then you will not go to the club. You went to the club.Each pair of statements represent true premises in a logical argument. Based on these premises, state a valid conclusion based on the form of the argument.
Denying the hypothesis: \(p \rightarrow q\) and \(\sim p\). Therefore, \(\sim q\).Use a truth table or construct a Venn diagram to prove whether the following arguments are valid.
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