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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

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. рла ялг рлr : per
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
Byron did not walk to the meeting or we started late.Use the fact that p → q is equivalent to ~ p ∨ q to write an equivalent form of the given statement.
A bobcat cannot purr, but a panther has 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 whether the statement is a tautology, self-contradiction, or neither.~ p ∧ (q ↔ ~ q)
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
Chase is not hiding or the pitcher is broken.Use the fact that p → q is equivalent to ~ p ∨ q to write an equivalent form of the given statement.
If your cell phone rings during class, then the teacher gets angry.Your cell phone does not ring during class.∴ The teacher does not get angry.(a) Translate the argument into symbolic form(b)
The sour cream is not cold if and only if the chili is spicy.Write the statement in symbolic form.Letp: The chili is spicy.q: The sour cream is cold.
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.(~ r ∨ p) ∨ q
Determine whether the statement is a tautology, self-contradiction, or neither.(p ∧ ~ q) ↔ ~ (p → q)
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
If Joanne goes to the Lightning game, then she will not go to the Rays game.Use the fact that p → q is equivalent to ~ p ∨ q to write an equivalent form of the given statement.
If the car is a Road Runner, then the car is fast.The car is fast.∴ The car is a Road Runner.(a) Translate the argument into symbolic form(b) Determine if the argument is valid or invalid. You may
If the chili is spicy, then the sour cream is not cold.Write the statement in symbolic form.Letp: The chili is spicy.q: The sour cream is cold.
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.~q ∨ ( r ∧ p)
Determine whether the statement is a tautology, self-contradiction, or neither.(~ q → p) ∨ ~ q
The Foo Fighters will practice or they will not sound good.Use the fact that p → q is equivalent to ~ p ∨ q to write an equivalent form of the given statement.
A grasshopper is an insect and a spider is not an insect.Use De Morgan’s laws, the fact that (p → q) ⇔ (~ p ∨ q), the fact that, ~ (p → q) ⇔ (p ∧ ~ q) truth tables, or equivalent
If we visit the zoo, then we see a zebra.We visit the zoo.ˆ´ We see a zebra.(a) Translate the argument into symbolic form(b) Determine if the argument is valid or invalid. You may compare
The chili is not spicy, but the sour cream is cold.Write the statement in symbolic form.Letp: The chili is spicy.q: The sour cream is cold.
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 ∨ q)
Determine whether the statement is a tautology, self-contradiction, or neither.(~ p ∨ q) ↔ (p ∧ ~ q)
Lynn Swann played for the Steelers or Jack Tatum played for the Raiders.Use De Morgan’s laws, the fact that (p → q) ⇔ (~ p ∨ q), the fact that, ~ (p → q) ⇔ (p ∧ ~ q) truth tables,
If I can get my child to preschool by 8:45 a.m., then I can take the 9:00 a.m. class.If I can take the 9:00 a.m. class, then I can be done by 2:00 p.m.∴ If I can get my child to
Determine the truth value for each simple statement. Then use these truth values to determine the truth value of the compound statement. 8 + 7 = 20 - 5 and 63/7 = 3 . 3
It is false that if we go to Chicago, then we will go to Navy Pier.Use the fact that ,~ (p → q) is equivalent to p ∧ ~ q to write the statement in an equivalent form.
It is false that the chili is spicy or the sour cream is cold.Write the statement in symbolic form.Letp: The chili is spicy.q: The sour cream is cold.
It is not true that Altec Lansing only produces speakers or Harman Kardon only produces stereo receivers.Use De Morgan’s laws, the fact that (p → q) ⇔ (~ p ∨ q), the fact that, ~ (p → q)
Determine whether the statement is an implication.~ p → p
If the guitar is a Les Paul model, then the guitar is made by Gibson.The guitar is not made by Gibson.∴ The guitar is not a Les Paul model.(a) Translate the argument into symbolic form(b)
Determine the truth value for each simple statement. Then use these truth values to determine the truth value of the compound statement.0 < - 3 or 5 ≥ 10
It is false that if General Electric makes the telephone, then the telephone is made in the United States.Use the fact that ,~ (p → q) is equivalent to p ∧ ~ q to write the statement in an
Travis Tritt did not win an Academy Award and Randy Jackson does not do commercials for Milk Bone Dog Biscuits.Use De Morgan’s laws, the fact that (p → q) ⇔ (~ p ∨ q), the fact that, ~ (p →
Determine whether the statement is an implication.p → (p ∨ q )
We will go for a bike ride or we will go shopping.We will not go shopping.∴ We will go for a bike ride.(a) Translate the argument into symbolic form(b) Determine if the argument is valid or
It is false that if the sour cream is not cold then the chili is spicy.Write the statement in symbolic form.Letp: The chili is spicy.q: The sour cream is cold.
Determine the truth value for each simple statement. Then use these truth values to determine the truth value of the compound statement.Chevrolet makes trucks or Toyota makes shoes.
I am cold and the heater is not working.Use the fact that ,~ (p → q) is equivalent to p ∧ ~ q to write the statement in an equivalent form.
Determine whether the statement is an implication.~ p → ~ (p ∧ q )
If we take the kayaks on the river, then we see alligators.We see alligators.∴ We take the kayaks on the river.(a) Translate the argument into symbolic form(b) Determine if the argument is
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBook~ q
Dell makes blue jeans and Apple makes computers.Determine the truth value for each simple statement. Then use these truth values to determine the truth value of the compound statement.
The Badgers beat the Nittany Lions and the Bucks beat the 76ers.Use the fact that ,~ (p → q) is equivalent to p ∧ ~ q to write the statement in an equivalent form.
If we go to the Rays game, then we will get Evan Longoria’s autograph.Write the (a) Converse, (b) Inverse (c) Contrapositive for the given statement.
Determine whether the statement is an implication.(p ∨ q ) → (p ∨ ~ r)
If you pass general chemistry, then you can take organic chemistry.You pass general chemistry.∴ You can take organic chemistry.(a) Translate the argument into symbolic form(b) Determine if
The New York Yankees are a baseball team and the New York Giants are a football team, but the Brooklyn Nets are not a basketball teamDetermine the truth value for each simple statement. Then use
It is not true that if Amazon has a sale then we will buy $100 worth of books.Use the fact that ,~ (p → q) is equivalent to p ∧ ~ q to write the statement in an equivalent form.
Determine whether the statement is an implication.[(p → q ) ∧ (q → p] → (p ↔ q)
Erica Kane will marry Samuel Woods or Erica Kane will marry David Hayward.Erica Kane will not marry Samuel Woods.∴ Erica Kane will marry David Hayward.(a) Translate the argument into symbolic
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBookp ^ q
Paris is in England or London is in France, and Berlin is in Germany.Determine the truth value for each simple statement. Then use these truth values to determine the truth value of the compound
Thompson is sick today but Allen didn’t go to school.Use the fact that, ~ (p → q) is equivalent to p ∧ ~ q to write the statement in an equivalent form.
If you do not advertise, then you do not sell more doughnuts.Write the (a) Converse, (b) Inverse (c) Contrapositive for the given statement.
Determine whether the statement is an implication.[(p ∨ q ) ∧ r] → (p ∨ q)
If you solve the New York Times crossword puzzle, then you are a genius.You are not a genius.∴ You did not solve the New York Times crossword puzzle.(a) Translate the argument into symbolic form(b)
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBookq ˆ¨ p
Chicago is in Mexico or Los Angeles is in California, or Dallas is in Canada.Determine the truth value for each simple statement. Then use these truth values to determine the truth value of the
If Nanette teaches macramé, then she needs extra yarn.Write the converse, inverse, and contrapositive of the statement in sentence form.
If the desk is made by Winner’s Only and the desk is in the Rose catalog, then we will not buy a desk at Miller’s Furniture.Write the (a) Converse, (b) Inverse (c) Contrapositive for the given
If p is true, q is false, and r is false, find the truth value of the statement.p → (q → r)
If it is cold, then graduation will be held indoors.If graduation is held indoors, then the fireworks will be postponed.∴ If it is cold, then the fireworks will be postponed.(a) Translate the
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBook~ p †’ q
Holstein is a breed of cattle and collie is a breed of dogs, or beagle is not a breed of cats.Determine the truth value for each simple statement. Then use these truth values to determine the truth
If the water is running, then Linus is getting a drink.Write the converse, inverse, and contrapositive of the statement in sentence form.
If you get straight A’s on your report card, then I will let you attend the prom.Write the (a) Converse, (b) Inverse (c) Contrapositive for the given statement.
If p is true, q is false, and r is false, find the truth value of the statement.(p ∧ ~ q ) → ~ r
If Lucinda is singing in the band, then Steve is playing the guitar.Lucinda is not singing in the band.∴ Steve is not playing the guitar.(a) Translate the argument into symbolic form(b)
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBook~ p †” ~q
India produced more feature films than the United States and China produced more feature films than JapanUse the table to determine the truth value of each simple statement. Then determine the value
If I go to Mexico, then I buy silver jewelry.Write the converse, inverse, and contrapositive of the statement in sentence form.
If p is true, q is false, and r is false, find the truth value of the statement.(p ∧ q )↔ (q ∨ ~ r)
Jevon is a bowler and Michael is a golfer.If Michael is a golfer, then Alisha is a curler. ∴ If Alisha is a curler, then Jevon is a bowler.(a) Translate the argument into symbolic form(b)
(a) If Cheap Trick plays at the White House, then Jacque is the president.(b) Cheap Trick does not play at the White House or Jacque is the president.(c) It is false that Cheap Trick plays at the
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBook~ p ˆ¨ ~ q
India produced more than twice as many feature films as the United States and India produced more feature films than Japan, China, and France combined.Use the table to determine the truth value of
If the sun is shining, then we take out the sailboat.Write the converse, inverse, and contrapositive of the statement in sentence form.
If p is true, q is false, and r is false, find the truth value of the statement.r → (~ p ↔ ~q)
Vitamin C helps your immune system or niacin helps reduce cholesterol.If niacin helps reduce cholesterol, then vitamin E enhances your skin.∴ Vitamin C helps your immune system and vitamin E
(a) The screwdriver is on the workbench if and only if the screwdriver is not on the counter.(b) If the screwdriver is not on the counter, then the screw-driver is not on the workbench.(c) It is
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBook~ (q ˆ¨ p)
The United States produced more feature films than Japan, but Japan produced more feature films than China.Use the table to determine the truth value of each simple statement. Then determine the
If the menu includes calzones, then I do not stay on my diet.Write the converse, inverse, and contrapositive of the statement in sentence form.
If p is true, q is false, and r is false, find the truth value of the statement.(~ p ∧ ~q) ∨ ~ r
It is snowing and I am going skiing.If I am going skiing, then I will wear a coat.∴ If it is snowing, then I will wear a coat.(a) Translate the argument into symbolic form(b) Determine if the
Determine which, if any, of the three statements are equivalent.(a) If 2 + 3 = 6, then 3 + 1= 5.(b) 2 + 3 = 6 if and only if 3 + 1 ≠ 5.(c) If 3 + 1 ≠ 5, then 2 + 3 ≠ 6.
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBook~ (p ˆ§ q)
Use the table to determine the truth value of each simple statement. Then determine the value of the compound statement.The United States produced more than twice as many feature films as France or
If Grandma is not available to babysit, then we cannot go to the movie.Write the converse, inverse, and contrapositive of the statement in sentence form.
If p is true, q is false, and r is false, find the truth value of the statement.~ [p →(q ∧ r)]
The garden has vegetables or the garden has flowers. If the garden does not have flowers, then the garden has vegetables.∴ The garden has flowers or the garden has vegetables(a)
(a) If the sale is on Tuesday and I have money, then I will go to the sale.(b) If I go to the sale, then the sale is on Tuesday and I have money.(c) I go to the sale, or the sale is on Tuesday and I
Write the compound statement in words.Letp: Joe has an iPad.q: Brie has a MacBook~q ˆ§ ~ p
The temperature is 90° and the air conditioner is not working, and the apartment is hot.Write the statements in symbolic form.Letp: The temperature is 90°.q: The air conditioner is working.r: The
It is false that 30% of Americans get 6 hours of sleep each night and 9% get 5 hours of sleep each night.Use the graph, which shows the number of hours Americans sleep, to determine the truth value
If a natural number is divisible by 14, then the natural number is divisible by 7.Write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement is
If p is true, q is false, and r is false, find the truth value of the statement.(~ p ↔ r) ∨ (~ q ↔ r)

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