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mathematics
a survey of mathematics with applications

Questions and Answers of A Survey of Mathematics with Applications

Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBook.~(q ∨ p)
If I write a haiku, then you write a sonnet.Write the converse, inverse, and contrapositive of the statement in sentence form.
Russia is larger than Canada and China is larger than Brazil.Use the table to determine the truth value of each simple statement. Then determine the truth value of the compound statement. Countries
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBook.~p ↔ ~q
If p is true, q is false, and r is false, determine the truth value of the statement.p → (q → r)
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBook.~p → q
If you got straight A’s, then you are on the president’s list.Write the converse, inverse, and contrapositive of the statement in sentence form.
Use a truth table to determine whether the statement is an implication.[(p ∨ q) ∧ r ] → (p ∨ q)
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBook.q ∨ p
Dexter works in Miami, but Debra does not work for him.Use the fact that ~(p → q) is equivalent to p ∧ ~q to write the statement in an equivalent form.
Determine the truth value for each simple statement. Then use these truth values to determine the truth value of the compound statement.George Washington was the first U.S. president or Abraham
Lucious will give the company to Hakeem or Lucious will give the company to Cookie.Lucious will not give the company to Hakeem.∴ Lucious will give the company to Cookie.(a) Translate the argument
Use a truth table to determine whether the statement is an implication.[(p → q) ∧ (q → p)] → (p ↔ q)
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBook.p ^ q
If Maya plays basketball, then she sits on the bench.Write the(a) Converse,(b) Inverse, (c) Contrapositive for the given statement.
Use a truth table to determine whether the statement is an implication.(p ∨ q) → (p ∨ ~r)
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBook.~p
Use a truth table to determine whether the statement is an implication.~p → ~(p ∧ q)
We did not go to the beach and we did not find sharks’ teeth.Use De Morgan’s laws, the fact that (p → q) ⇔ (~p ∨ q), or the fact that ~(p → q) ⇔ (p ∧ ~q), to write an equivalent
Use a truth table to determine whether the statement is an implication.p → (p ∨ q)
It is not true that if Ghana is in the United Nations then Ghana is in the World Trade Organization.Use the fact that ~(p → q) is equivalent to p ∧ ~q to write the statement in an equivalent form.
It is false that if the tacos are not vegan then the burrito contains sriracha.Write the statement in symbolic form.Letp: The burrito contains sriracha.q: The tacos are vegan.
It is false that the burrito contains sriracha or the tacos are vegan.Write the statement in symbolic form.Letp: The burrito contains sriracha.q: The tacos are vegan.
Use a truth table to determine whether the statement is an implication.~p → p
The burrito does not contain sriracha or the tacos are not vegan.Write the statement in symbolic form.Letp: The burrito contains sriracha.q: The tacos are vegan.
Determine the truth value of the statement ifa) p is true, q is false, and r is true.b) p is false, q is true, and r is true.(~r ∧ ~q) ∧ (~r ∨ ~p)
If we visit Harlem, then we go to the Apollo Theater.If we go to the Apollo Theater, then we see a concert.∴ If we visit Harlem, then we see a concert.(a) Translate the argument into symbolic
Use a truth table to determine whether the statement is a tautology, self contradiction, or neither.~[(p ∧ q) → p]
The tacos are not vegan if and only if the burrito contains sriracha.Write the statement in symbolic form.Letp: The burrito contains sriracha.q: The tacos are vegan.
Determine the truth value of the statement ifa) p is true, q is false, and r is true.b) p is false, q is true, and r is true.(~p ∨ ,q) ∨ (~r ∨ q)
Use a truth table to determine whether the statement is a tautology, self contradiction, or neither.~[(p ∨ q) ↔ q]
Opal exercises daily or she is not healthy.Use the fact that p → q is equivalent to ,p ∨ q to write an equivalent form of the given statement.
If the burrito does not contain sriracha, then the tacos are vegan.Write the statement in symbolic form.Letp: The burrito contains sriracha.q: The tacos are vegan.
Determine the truth value of the statement ifa) p is true, q is false, and r is true.b) p is false, q is true, and r is true.~q ∨ (r ∧ p)
Use a truth table to determine whether the statement is a tautology, self contradiction, or neither.(p ∨ ~q) ∨ (~p ∨ q)
The burrito contains sriracha and the tacos are not vegan.Write the statement in symbolic form.Letp: The burrito contains sriracha.q: The tacos are vegan.
Determine the truth value of the statement ifa) p is true, q is false, and r is true.b) p is false, q is true, and r is true.(~r ∧ p) ∨ q
If the Rays win the division, then the Rays go to the playoffs.The Rays do not win the division.∴ The Rays do not go to the playoffs.(a) Translate the argument into symbolic form (b) Determine
Use a truth table to determine whether the statement is a tautology, self contradiction, or neither.(~p ∧ q) ∧ (p ∨ ~q)
Determine the truth value of the statement ifa) p is true, q is false, and r is true.b) p is false, q is true, and r is true.(p ∧ ~q) ∨ r
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table.Data From argument to a standard form: p V ~q q V ~r r V V ~p :p vr
Use a truth table to determine whether the statement is a tautology, self contradiction, or neither.~p ∧ (p ∧ q)
If I see a movie, then I buy popcorn.Use the fact that p → q is equivalent to ,p ∨ q to write an equivalent form of the given statement.
Determine the truth value of the statement ifa) p is true, q is false, and r is true.b) p is false, q is true, and r is true.(p ∨ ,q) ∧ [~( p ∧ ,r)]
Use a truth table to determine whether the statement is a tautology, self contradiction, or neither.~p ∨ (p ∨ q)
Determine the truth value of the statement ifa) p is true, q is false, and r is true.b) p is false, q is true, and r is true.~p ∧ (~q ∨ ~r)
It is false that if you play spider solitaire, then you do not play free cell and you play minesweeper.Write the statement in symbolic form. Then construct a truth table for the symbolic statement.
If I am late for class, then I will not get bonus points or I will fail the test.Use De Morgan’s laws to write an equivalent statement for the given sentence.
Franklin is wealthy, but he is not famous.Use De Morgan’s laws to write an equivalent statement for the given sentence.
Use an Euler diagram to determine whether the syllogism is valid or invalid.All cats are dogs.All dogs are cows.All cows are pigs.∴ All cats are pigs.
Determine the truth value of the statement ifa) p is true, q is false, and r is true.b) p is false, q is true, and r is true.p ∧ (~q ∨ r)
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table.Data From argument to a standard form: b- :p-r
Use an Euler diagram to determine whether the syllogism is valid or invalid.All sweet things taste good.All things that taste good are fattening.All things that are fattening put on pounds.∴ All
Determine the truth value of the statement ifa) p is true, q is false, and r is true.b) p is false, q is true, and r is true.(p ∧ ~q) ∨ r
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table.Data From argument to a standard form: q Vr .. r
Blackberries are high in vitamin K if and only if mangos are high in B vitamins, or cherries are high in vitamin C.Write the statement in symbolic form. Then construct a truth table for the symbolic
Use an Euler diagram to determine whether the syllogism is valid or invalid.All Zebras are pens.A Ticonderoga is not a pen.∴ A Ticonderoga is not a Zebra.
The drier is loud or I am drying shoes, and I cannot fix dinner.Write the statement in symbolic form and construct a truth table.
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table.Data From argument to a standard form: →r
Jana is the CEO if and only if Allia is the CFO, or Camila is not the COO.Write the statement in symbolic form. Then construct a truth table for the symbolic statement.
It is false that Jay-Z sings opera and Beyoncé sings country.Use De Morgan’s laws to write an equivalent statement for the given sentence.
Use an Euler diagram to determine whether the syllogism is valid or invalid.All Rolexes are watches.A Pulsar is not a Rolex.∴ A Pulsar is not a watch.
School is not in session and the kids are home, or I am working.Write the statement in symbolic form and construct a truth table.
Determine whether the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.Data From argument to a standard form: :p Vr
Use an Euler diagram to determine whether the syllogism is valid or invalid.All rainy days are cloudy.Today it is cloudy.∴ Today is a rainy day.
Write the statement in symbolic form and construct a truth table.It is false that Charlie is not a tiger or Patty is a dolphin.
Determine whether the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.Data From argument to a standard form: →y .. ~y
If a minute has 60 seconds, then an hour has 60 minutes if and only if a day has 20 hours.Determine the truth value of the statement. You may need to use the Internet as a reference.
Construct a truth table for the statement.(~p ↔ ~q) → (~q ↔ r)
Use an Euler diagram to determine whether the syllogism is valid or invalid.Some nurses work in pediatrics.Seth works in pediatrics.∴ Seth is a nurse.
It is false that the car is not a Chevrolet, but the car is a Corvette.Write the statement in symbolic form and construct a truth table.
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table.Data From argument to a standard form: y .. x
Construct a truth table for the statement.(p → q) ↔ (~q → ~r)
Use an Euler diagram to determine whether the syllogism is valid or invalid.No squirrels are reptiles.No reptiles are birds.∴ No squirrels are birds.
Katie will not go to the zoo or she will go to the library.Write the statement in symbolic form and construct a truth table.
Construct a truth table for the statement.(p ∧ q) → ~r
Construct a truth table for the statement.(p ∨ ~q) ↔ r
Joaquin will pitch or he will not play first base.Write the statement in symbolic form and construct a truth table.
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table.Data From argument to a standard form: t - u .. -t
Construct a truth table for the statement.p → (q ∧ ~r)
Construct a truth table for the statement.(~p ∧ q) → ~r
All Apple smartphones run on an IOS operating system. Write the negation of the statement.
Sophia did not work today, but she volunteered at the shelter. Write the statement in symbolic form and construct a truth table.
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table.Data From argument to a standard form: .. S
Construct a truth table for the statement.p ∧ (~q ∨ r)
Construct a truth table for the statement.(~p ↔ q) ∨ ~r
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table.Data From argument to a standard form: ... n
Construct a truth table for the statement.(p ∨ q) ↔ (p ∨ r)
Construct a truth table for the statement.~p ↔ (q ∨ ~r)
Draw a switching circuit that represents the symbolic statement.[(p ∨ q) ∨ (r ∧ q)] ∧ (~p)
No freshmen can participate in the graduation ceremonies. Write the negation of the statement.
Use an Euler diagram to determine whether the syllogism is valid or invalid.Some chemicals are poisonous.Some poisonous things are beautiful.∴ Some chemicals are beautiful.
Construct a truth table for the statement.~p ∨ (~q ∧ r)
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table.Data From argument to a standard form: 1- m ~ m
Construct a truth table for the statement.q ↔ (p ∨ ~q)
Construct a truth table for the statement.(~p → q) ∧ r
All Eco Sun scooters are made by Amigo.Write the negation of the statement.
Use an Euler diagram to determine whether the syllogism is valid or invalid.Some stamps are collectors’ items.Some collectors’ items are valuable.∴ Some stamps are valuable.
All coffee beans contain caffeine.Write the negation of the statement.
Construct a truth table for the statement.(~p ∧ q) ∨ ~r

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