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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

Nick played football and Max played baseball.Write the negation of the statement.
All houses are wired using parallel circuits.Write the negation of the statement.
Construct a truth table for the statement.(r ∧ q) ∧ ~ p
Construct a truth table for the statement.(p ∨ q) ↔ (p ∨ r)
Construct a truth table for the statement.~ p ↔ (q ∨ r)
Use De Morgan’s laws to determine whether the two statements are equivalent.~ ( p ∨ q), ~ p ∧ ~ q
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table. п — о .. n
Draw a switching circuit that represents the symbolic statement.[(p ∨ q) ∨ (r ∧ q)] ∧ (~ p)
Some flowers love sunlight.All things that love sunlight love water.∴ Some flowers love water.Use an Euler diagram to determine whether the syllogism is valid or invalid.
Write the converse, inverse, and contrapositive of the conditional statement “If the garbage truck comes, then today is Saturday.”
Some turtles do not have claws.Write the negation of the statement.
Apples are a good source of fiber and oranges are a good source of vitamin.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 ∧ r) → (q ∨ r)
Use De Morgan’s laws to determine whether the two statements are equivalent.~ ( p ∨ q), ~ p ∨ ~ q
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table. rs
All rainy days are cloudy.Today it is cloudy.∴ Today is a rainy dayUse an Euler diagram to determine whether the syllogism is valid or invalid.
Draw a switching circuit that represents the symbolic statement.[(p ∨ q) ∧ r] ∨ (~ p ∧ q)
Some caterpillars are furry.All furry things are mammals.ˆ´ Some caterpillars are mammals.Use an Euler diagram to determine whether the syllogism is valid or invalid.
Construct a diagram of a circuit that corresponds to(p ∧ q) ∨ (~ p ∨ ~ q)
No Capricorns are Leos.Write the negation of the statement.
Mr. Hart got his car started, but he was late for class.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.(~ r ∨ ~ q) ∨ ~ p)] → p
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table. t-u . -u
Represent each circuit with a symbolic statement. Then use a truth table to determine if the circuits are equivalent.
No scarecrows are tin men.No tin men are lions.∴ No scarecrows are lions.Use an Euler diagram to determine whether the syllogism is valid or invalid.
No bicycles have three wheels.Write the negation of the statement.
I have worked all week, but I have not been paid.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.[r ∧ (q ∨ ~ p)] ↔ ~ p
Use De Morgan’s laws to determine whether the two statements are equivalent.~ (~ p ∧ q), p ∨ ~ q
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table.
Represent each circuit with a symbolic statement. Then use a truth table to determine if the circuits are equivalent. b.
No squirrels are reptiles.No reptiles are birds.∴ No squirrels are birds.Use an Euler diagram to determine whether the syllogism is valid or invalid.
All horses have manes.Write the negation of the statement.
It is false that Mr. Farinelli is the president or that Ms. Chow is the treasurer.Write the statement in symbolic form and construct a truth table.
Construct a truth table for the statement.(p → q) ↔ (~ q → r)
Apple makes iPhones and Dell makes canoes, or Hewlett Packard makes laser printers.Determine the truth value of the statement. You may need to use a reference such as the Internet or an encyclopedia.
Use De Morgan’s laws to determine whether the two statements are equivalent.(~ p ~ ∨ q) → r, ~ (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. х—у y z . х—z
Represent each circuit with a symbolic statement. Then use a truth table to determine if the circuits are equivalent. b.
Some dogs wear glasses.Fido wears glasses.∴ Fido is a dogUse an Euler diagram to determine whether the syllogism is valid or invalid.
It is false that Jasper is a tutor and Mark is a secretary.Write the statement in symbolic form and construct a truth table.
Construct a truth table for the statement.(~ p ↔ ~ q) → (~ q ↔ r)
If ESPN is a sports network then CNN is a news network, if and only if Nickelodeon is a cooking network.Determine the truth value of the statement. You may need to use a reference such as the
Use De Morgan’s laws to determine whether the two statements are equivalent.q → ~ (p ∧ ~ r ), q → ~ p ∨ r
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table. х .. ~y
Represent each circuit with a symbolic statement. Then use a truth table to determine if the circuits are equivalent. b.
Some teachers are not professors.Write the negation of the statement.
Mike made pizza and Dennis made a chef salad, but Gil burned the lemon squares.Write the statement in symbolic form and construct a truth table.
If Oregon borders the Pacific Ocean or California borders the Atlantic Ocean, then Minnesota is south of Texas.Determine the truth value of the statement. You may need to use a reference such
If today is Monday, then the library is open and we can study together.Write the statement in symbolic form. Then construct a truth table for the symbolic statement.
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table. ред ялr
It is false that Taylor Swift is a country singer and Wiz Khalifa sings opera.Use De Morgan€™s laws to write an equivalent statement for the given sentence. Taylor Swift
Represent each circuit with a symbolic statement. Then use a truth table to determine if the circuits are equivalent.
All sweet things taste good.All things that taste good are fattening.All things that are fattening put on pounds.∴ All sweet things put on pounds.Use an Euler diagram to determine whether the
No mountain climbers are teachers. Write the negation of the statement.
The copier is out of toner, or the lens is dirty or the corona wires are broken.Write the statement in symbolic form and construct a truth table.
President’s Day is in February, or Memorial Day is in May and Labor Day is in December.Determine the truth value of the statement. You may need to use a reference such as the Internet or an
We will advance in the tournament if and only if Max plays, or Pondo does not show up.Write the statement in symbolic form. Then construct a truth table for the symbolic statement.
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table. .:~r→~p
It is false that the Camaro is a Dodge or the Challenger is a Chevy.Use De Morgan’s laws to write an equivalent statement for the given sentence.
Represent each circuit with a symbolic statement. Then use a truth table to determine if the circuits are equivalent. b.
All cats are dogs.All dogs are cows.All cows are pigs.∴ All cats are pigs.Use an Euler diagram to determine whether the syllogism is valid or invalid.
I am hungry, and I want to eat a healthy lunch and I want to eat in a hurry.Write the statement in symbolic form and construct a truth table.
Determine the truth value of the statement when p is T, q is F, and r is F.(~ p ∨ q) → ~ (p ∧ ~ q)
The election was fair if and only if the polling station stayed open until 8 p.m., or we will request a recount.Write the statement in symbolic form. Then construct a truth table for the symbolic
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table. ~рла
The dog was not a bulldog and the dog was not a boxer.Use De Morgan’s laws to write an equivalent statement for the given sentence.
Explain why the lightbulb will never go on in the following circuit. р
Can an argument be valid if the conclusion is a false statement? Explain your answer.
Determine the truth value of the statement if(a) 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 the truth value of the statement when p is T, q is F, and r is F.(p ↔ q) → (~ p ∨ r)
If the dam holds then we can go fishing, if and only if the pole is not broken.Write the statement in symbolic form. Then construct a truth table for the symbolic statement.
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, given on pageIs the argument valid or invalid? Invalid Valid PV q Invalid r^ p :. 9
The pot roast is hot, but it is not well done.Use De Morgan’s laws to write an equivalent statement for the given sentence.
Explain why the lightbulb will always be on in the following circuit.
Can an argument be invalid if the conclusion is a true statement? Explain.
A panther has a long tail and a bobcat can purr.Write the statement in symbolic form.Letp: A panther has a long tail.q: A bobcat can purr.
Determine the truth value of the statement if(a) 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 the truth value of the statement when p is T, q is F, and r is F.~ r ↔ [(p ∨ q) ↔ ~ p]
If it is not too cold then we can take a walk, or we can go to the gym.Write the statement in symbolic form. Then construct a truth table for the symbolic statement.
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table. q Vr
If Ashley takes the new job, then she will not move or she will buy a new house in town.Use De Morgan’s laws to write an equivalent statement for the given sentence.
Design a circuit that can be represented by(a) p → q(b) ~ (p → q)
Statements in logic can be translated into set statements: For example, p ˆ§ q is similar to P ˆ© Q; p ˆ¨ q is similar to P ˆª Q;and p †’ q is
A bobcat cannot purr or a panther does not have a long tail.Write the statement in symbolic form.Letp: A panther has a long tail.q: A bobcat can purr.
Determine the truth value of the statement if(a) 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 the truth value of the statement when p is T, q is F, and r is F.~ [(q ∧ r) → (~ p ∨ r)]
It is false that if Elaine went to lunch, then she cannot take a message and we will have to go home.Write the statement in symbolic form. Then construct a truth table for the symbolic statement.
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table. b. 9 — г . рәг
If Phil buys us dinner, then we will not go to the top of the CN Tower but we will be able to walk to the Red Bistro Restaurant.Use De Morgan’s laws to write an equivalent statement for the given
Determine the truth value of the statement if(a) 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 pairs of statements are equivalent. You may use De Morgan’s laws, the fact that (p → q) ⇔ (~ p ∨ q), the fact that, ~ (p → q) ⇔ (p ∧ ~ q) truth tables, or
Determine whether the statement is a tautology, self-contradiction, or neither.(p ∧ q) ∨ ~ q
Determine whether the argument is valid or invalid. You may compare the argument to a standard form, or use a truth table. p V r .. q V ~p
If Janette buys a new car, then she sells her old car.Use the fact that p → q is equivalent to ~ p ∨ q to write an equivalent form of the given statement.
If a panther does not have a long tail, then a bobcat cannot purr.Write the statement in symbolic form.Letp: A panther has a long tail.q: A bobcat can purr.
Determine the truth value of the statement if(a) 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)]

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