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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

If you read The Riptide Ultra-Glide then you can under-stand Tiger Shrimp Tango. You cannot understand Tiger Shrimp Tango. Therefore, you did not read The Riptide Ultra-Glide.Translate the argument
Determine whether the argument is valid or invalid. You may compare the argument to a standard form or use a truth table. d-
The temperature is not 90° and the air conditioner is working, but the apartment is hot.Write the statements in symbolic form.Letp: The temperature is 90°.q: The air conditioner is working.r: The
Twenty-five percent of Americans get 6 hours of sleep each night, and 30% get 7 hours of sleep each night or 9% do not get 5 hours of sleep each night.Use the graph, which shows the number of hours
If the quadrilateral is a parallelogram, then the opposite sides are parallel.Write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement is true
If p is true, q is false, and r is false, find the truth value of the statement.~[ (p ∨ q) ↔ (p → ~ r)]
The printer has a clogged nozzle or the printer does not have toner. The printer has toner. Therefore, the printer has a clogged nozzle.
Determine whether the argument is valid or invalid. You may compare the argument to a standard form or use a truth table. рла →r
The temperature is 90° and the air conditioner is working, or the apartment is hot.Write the statements in symbolic form.Letp: The temperature is 90°.q: The air conditioner is working.r: The
Thirteen percent of Americans get 5 or fewer hours of sleep each night or 32% get 6 or more hours of sleep each night, and 30% get 8 or more hours of sleep each night.Use the graph, which shows the
If a natural number is divisible by 3, then the natural number is divisible by 6.Write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement is
Determine the truth value for each simple statement. Then, using the truth values, determine the truth value of the compound statement.If 92 = 81, then √81= 9
Max is playing Game Boy with the sound off or Max is wearing headphones. Max is not playing Game Boy with the sound off. Therefore, Max is wearing head-phones.Translate the argument into symbolic
If Jose is the manager, then Kevin is the coach.If Kevin is the coach, then Tim is the umpire.∴ If Jose is the manager, then Tim is the umpire.Determine whether the argument is valid or invalid.
Over one-half of Americans get 7 or fewer hours of sleep each night, and over one-quarter get 6 or fewer hours of sleep each night.Use the graph, which shows the number of hours Americans sleep, to
If 1/n is not a natural number, then n is not a natural number.Write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement is true or false.
Determine the truth value for each simple statement. Then, using the truth values, determine the truth value of the compound statement.If 5 < 1, then 7 >10.
If the cat is in the room, then the mice are hiding. The mice are not hiding. Therefore, the cat is not in the room.Translate the argument into symbolic form. Then determine whether the argument is
If the truck is a diesel, then the truck is too cold to start. The truck is too cold to start or the car has a flat tire. Therefore, the truck is not a diesel.Determine whether the argument is valid
If the apartment is hot and the air conditioner is working, then the temperature is 90°.Write the statements in symbolic form.Letp: The temperature is 90°.q: The air conditioner is working.r: The
Tanisha owns a convertible or Joan does not own a Volvo.Letp: Tanisha owns a convertible.q: Joan owns a Volvo.Translate each statement into symbols. Then construct a truth table for each compound
If two lines do not intersect in at least one point, then the two lines are parallel.Write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement
If a cat has whiskers or a fish can swim, then a dog lays eggs.Determine the truth value for each simple statement. Then, using the truth values, determine the truth value of the compound statement.
A tiger is a cat and a giraffe is a dog. A tiger is not a cat or a giraffe is not a dog. Therefore, a tiger is not a cat.Translate the argument into symbolic form. Then determine whether the argument
All marigolds are annuals.Some tulips are annuals.∴ Some tulips are marigolds.Use an Euler diagram to determine whether the argument is valid or invalid.
The temperature is not 90° if and only if the air conditioner is not working, or the apartment is not hot.Write the statements in symbolic form.Letp: The temperature is 90°.q: The air conditioner
Tanisha does not own a convertible, but Joan owns a Volvo.Letp: Tanisha owns a convertible.q: Joan owns a Volvo.Translate each statement into symbols. Then construct a truth table for each compound
Write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement is true or false.If m · a/m · b ≠ a/b, then m is not a counting number.
If the moon circles the earth and the earth circles the sun, then the moon is made of cheese.Determine the truth value for each simple statement. Then, using the truth values, determine the truth
If Bonnie passes the bar exam, then she will practice law. Bonnie will not practice law. Therefore, Bonnie did not pass the bar exam.Translate the argument into symbolic form. Then determine whether
All hackysack players are students.Joel is a hackysack player.∴ Joel is a student.Use an Euler diagram to determine whether the argument is valid or invalid.
The apartment is hot if and only if the air conditioner is working, and the temperature is 90°.Write the statements in symbolic form.Letp: The temperature is 90°.q: The air conditioner is
Tanisha owns a convertible or Joan does not own a Volvo.Letp: Tanisha owns a convertible.q: Joan owns a Volvo.Translate each statement into symbols. Then construct a truth table for each compound
(a) If the player gets a red card, then the player sits out.(b) If the player sits out, then the player gets a red card.(c) The player does not sit out or the player gets a red card.Determine which,
Apple makes computers, if and only if Nike makes sports shoes or Rolex makes watches.Determine the truth value for each simple statement. Then, using the truth values, determine the truth value of
The baby is crying but the baby is not hungry. If the baby is hungry then the baby is crying. Therefore, the baby is hungry.Translate the argument into symbolic form. Then determine whether the
No Beatles are Rolling Stones. Some Rolling Stones are Small Faces.∴ No Beatles are Small Faces.Use an Euler diagram to determine whether the argument is valid or invalid.
If the air conditioner is working, then the temperature is 90° if and only if the apartment is hot.Write the statements in symbolic form.Letp: The temperature is 90°.q: The air conditioner is
Tanisha does not own a convertible or Joan does not own a Volvo.Letp: Tanisha owns a convertible.q: Joan owns a Volvo.Translate each statement into symbols. Then construct a truth table for each
(a) If Fido is our dog’s name, then Rex is not our dog’s name.(b) It is false that Fido is our dog’s name and Rex is not our dog’s name.(c) Fido is not our dog’s name or Rex is our dog’s
Spike Lee is a movie director, or if Halle Berry is a school teacher then George Clooney is a circus clownDetermine the truth value for each simple statement. Then, using the truth values, determine
If the car is new, then the car has air conditioning. The car is not new and the car has air conditioning. Therefore, the car is not new.Translate the argument into symbolic form. Then determine
All bears are furry.Teddy is furry.∴ Teddy is a bear.Use an Euler diagram to determine whether the argument is valid or invalid.
Write each symbolic statement in words.Letp: The water is 70°.q: The sun is shining.r: We go swimming.(p ∨ q) ∧ ~ r
The car is run by electric power or the heat is solar generated, but the house is owned by an engineer.Letp: The house is owned by an engineer.q: The heat is solar generated.r: The car is run by
(a) The shoes are not on sale but the purse is on sale.(b) If the shoes are not on sale then the purse is not on sale.(c) It is false that the shoes are on sale or the purse is not on sale.Determine
If you liked This Is Spinal Tap then you liked Best in Show. If you liked Best in Show then you did not like A Mighty Wind. Therefore, if you liked This Is Spinal Tap then you liked A Mighty
(a) Write the corresponding symbolic statement of the circuit shown.(b) Construct a truth table to determine when the lightbulb will be on. b.
Write each symbolic statement in words.Letp: The water is 70°.q: The sun is shining.r: We go swimming.(p ∧ q) ∨ r
The house is owned by an engineer and the heat is solar generated, or the car is run by electric power.Letp: The house is owned by an engineer.q: The heat is solar generated.r: The car is run by
(a) Cher did not sing “Believe” or Sting did not sing “Russians.”(b) If Cher sang “Believe” then Sting sang “Russians.”(c) It is false that Sting sang “Russians” and Cher did not
Honda makes automobiles or Honda makes motorcycles, if and only if Mazda makes cereal.Determine the truth value for each simple statement. Then, using the truth values, determine the truth value of
The engineering courses are difficult and the chemistry labs are long. If the chemistry labs are long, then the art tests are easy. Therefore, the engineering courses are difficult and the art tests
Construct a diagram of a circuit that corresponds to the symbolic statement (p ∨ q) ∨ (p ∧ q).
Write each symbolic statement in words.Letp: The water is 70°.q: The sun is shining.r: We go swimming.~ p ∧ (q ∨ r)
The heat is solar generated, or the house is owned by an engineer and the car is not run by electric power.Letp: The house is owned by an engineer.q: The heat is solar generated.r: The car is run by
(a) We do not go hiking or we go fishing.(b) If we go hiking, then we do not go fishing.(c) If we go fishing, then we do not go hiking.Determine which, if any, of the three statements are equivalent.
Io has a diameter of 1000 €“3161 miles or Thebe may have water, and Io may have atmosphere.Use the information provided about the moons for the planets Jupiter and Saturn to determine the
Determine whether the circuits shown are equivalent.
Use the following information to arrive at your answers. Many restaurant dinner menus include statements such as the following: All dinners are served with a choice of: soup or salad, and potatoes or
If the radio is a Superadio, then the radio is made by RCA.The radio is a Superadio. Therefore, . . .Using the standard forms of arguments and other information you have learned, supply what you
To qualify for a loan of $45,000, an applicant must have a gross income of $30,000 if single, $50,000 combined in-come if married, and assets of at least $10,000.Mr. Argento, married with two
Write each symbolic statement in words.Letp: The water is 70°.q: The sun is shining.r: We go swimming.(q → p) ∨ r
The house is not owned by an engineer, and the car is not run by electric power and the heat is solar generated.Letp: The house is owned by an engineer.q: The heat is solar generated.r: The car is
(a) If Tim is the director then Johnny is the actor.(b) Tim is not the director or Johnny is the actor.(c) It is false that Tim is the director and Johnny is not the actorDetermine which, if any, of
Titan may have water and Titan may have atmosphere, if and only if Janus may have water.Use the information provided about the moons for the planets Jupiter and Saturn to determine the truth values
If the temperature hits 100°, then we will go swimming.We did not go swimming.Therefore, . . .Using the standard forms of arguments and other information you have learned, supply what you believe is
Write each symbolic statement in words.Letp: The water is 70°.q: The sun is shining.r: We go swimming.~ r → (q ∧ p)
To qualify for a loan of $40,000, an applicant must have a gross income of $28,000 if single, $46,000 combined income if married, and assets of at least $6,000.Mrs. Rusinek, married with three
(a) The grass grows and the trees are blooming.(b) If the trees are blooming, then the grass does not grow.(c) The trees are not blooming or the grass does not grow.Determine which, if any, of the
Phoebe has a larger diameter than Rhea if and only if Callisto may have water ice, and Calypso has a diameter of 6 €“ 49 miles.Use the information provided about the moons for the planets
I am stressed out or I have the flu.I do not have the flu.Therefore, . . .Using the standard forms of arguments and other information you have learned, supply what you believe is a logical conclusion
Write each symbolic statement in words.Letp: The water is 70°.q: The sun is shining.r: We go swimming.(q ∧ r) → p
(a) Mr. Patrick is chosen as department chair if and only if he is the only candidate.(b) If Mr. Patrick is chosen as department chair then he is the only candidate, and if Mr. Patrick is the only
If Jupiter has 16 moons or Saturn does not have 18 moons, then Saturn has 7 moons that may have water ice.Use the information provided about the moons for the planets Jupiter and Saturn to determine
If I can get Nick to his piano lesson by 3:30 p.m., then I can do my shopping.If I can do my shopping, then we do not need to order pizza again.Therefore, . . .Using the standard forms of
Write each symbolic statement in words.Letp: The water is 70°.q: The sun is shining.r: We go swimming.(q → r) ∧ p
An airline advertisement states, €œTo get the special fare you must purchase your tickets between January 1 and February 15 and fly round trip be-tween March 1 and April 1. You must depart
(a) If the corn bag goes in the hole, then you are awarded three points.(b) It is false that the corn bag goes in the hole and you are awarded three points.(c) The corn bag does not go in the hole
The number of communications credits needed is more than the number of mathematics credits needed and the number of cultural issues credits needed is equal to the number of humanities credits needed,
If you close the deal, then you will get a commission.You did not get a commission.Therefore, . . .Using the standard forms of arguments and other information you have learned, supply what you
Write each symbolic statement in words.Letp: The water is 70°.q: The sun is shining.r: We go swimming.~ p → (q ∨ r)
Use the following information to arrive at your answers. Many restaurant dinner menus include statements such as the following: All dinners are served with a choice of: soup or salad, and potatoes or
If Muhundan received the outstanding teacher award, then Muhundan spoke at the teachers’ conference.Suppose both of the following statements are false.p: Muhundan spoke at the teachers’
(a) Fitz and the Tantrums will not go on tour if and only if James King does not play the saxophone.(b) It is false that Fitz and the Tantrums will go on tour if and only if James King does not play
Construct a truth table for the symbolic statement.~[(~ (p ∨ q)) ∨ (q ∧ r)]
If the number of elective credits needed is 21 or the number of communications credits needed is 15, then the number of humanities credits needed is equal to the number of mathematics credits
If Katherine is at her ballet lesson, then Allyson will take a nap.Katherine is at her ballet lesson. Therefore, . . . Using the standard forms of arguments and other information you
Is it possible for an argument to be valid if its conclusion is false? Explain your answer.
Write each symbolic statement in words.Letp: The water is 70°.q: The sun is shining.r: We go swimming.(q ↔ p) ∧ r
Construct a truth table for the symbolic statement.[(q ∧ ~ r) ∧ (~p ∨ ~ q)] ∨ (p ∨ ~ r)
(a) If the pay is good and today is Monday, then I will take the job.(b) If I do not take the job, then it is false that the pay is good or today is Monday.(c) The pay is good and today is Monday, or
Is it possible for an argument to be invalid if its conclusion is true? Explain your answer.
Write each symbolic statement in words.Letp: The water is 70°.q: The sun is shining.r: We go swimming.q → (p ↔ r)
On page 107, we indicated that a compound statement consisting of n simple statements had 2n distinct true–false cases.(a) How many distinct true–false cases does a truth table containing simple
(a) If you are 18 years old and a citizen of the United States, then you can vote in the presidential election.(b) You can vote in the presidential election, if and only if you are a citizen of the
If Muhundan did not receive the outstanding teacher award, then Muhundan spoke at the teachers’ conference.Suppose both of the following statements are false.p: Muhundan spoke at the
Is it possible for an argument to be invalid if the premises are all true? Explain your answer.
(a) The package was sent by Federal Express, or the pack-age was not sent by United Parcel Service but the pack-age arrived on time.(b) The package arrived on time, if and only if the package was
Must (p ∧ ~ q) ∨ r and (q ∧ ~ r) ∨ p have the same number of trues in their answer columns Explain.

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