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nature of mathematics

Questions and Answers of Nature Of Mathematics

The following sentence is found on a tax form:If you do not itemize deductions on Schedule A and you have charitable contributions, then complete the worksheet on page 14 and enter the allowable part
Assume p is F and q is T. Under these assumptions, which of the statements in Problem 32 are true?Data from Problem 32Let p: Today is Friday; q: There is homework tonight. Translate each of the
Let p: Today is Friday; q: There is homework tonight. Translate each of the following statements into words.a. p ∧ qb. ∼p ∧ qc. p ∨ ∼qd. ∼p ∨ ∼q
Let p: Prices will rise; q: Taxes will rise. Translate each of the following statements into words.a. p ∨ q Prices or taxes will rise.b. ∼p ∧ q Prices will not rise and taxes will rise.c. p
Assume that prices rise and taxes do not rise. Under these assumptions, which of the statements in Problem 28 are true?Data from Problem 28Let p: Prices will rise; q: Taxes will rise. Translate each
Assume that prices rise and taxes also rise. Under these assumptions, which of the statements in Problem 28 are true?
Let p: Prices will rise; q: Taxes will rise. Translate each of the following statements into symbols.a. Prices will rise, or taxes will not rise.b. Prices will rise, and taxes will not
Some integers are not odd.Write the negation of each statement in Problems 20–27.
Some apples are rotten.Write the negation of each statement in Problems 20–27.
All counting numbers are divisible by 1.Write the negation of each statement in Problems 20–27.
All squares are rectangles.Write the negation of each statement in Problems 20–27.
No triangles are squares.Write the negation of each statement in Problems 20–27.
No even integers are divisible by 5.Write the negation of each statement in Problems 20–27.
All dogs have fleas.Write the negation of each statement in Problems 20–27.
All mathematicians are ogres.Write the negation of each statement in Problems 20–27.
Use Figure 3.2 to decide whether each of the statements in Problems 15–19 is true or false.Figure 3.2Not everyone who has a beard also has a mustache. Harry S. Truman (Democrat) 1945-1953 Hulton
Use Figure 3.2 to decide whether each of the statements inProblems 15–19 is true or false.Figure 3.2There are two black presidents. Harry S. Truman (Democrat) 1945-1953 Hulton Archive/Getty Images
Answer the questions in Problems 9–14 about the presidents shown in Figure 3.2.Figure 3.2Who is balding and has a mustache? Harry S. Truman (Democrat) 1945-1953 Hulton Archive/Getty Images Barack
Answer the questions in Problems 9–14 about the presidents shown in Figure 3.2.Figure 3.2Who is black and does not wear glasses? Harry S. Truman (Democrat) 1945-1953 Hulton Archive/Getty Images
According to the definition, which of the examples in Problems 5–8 are statements?a. Hickory, Dickory, Dock, the mouse ran up the clock.b. 3 + 5 = 9c. Is John ugly?d. John has a wart on the end
Translate the given word statements into symbolic form, using only simple statements as variables.a. I will not attend a hockey game.b. I will go to the hockey game and will not enjoy it.c. I will
A man is about to be electrocuted but is given a chance to save his life. In the execution chamber are two chairs, labeled 1 and 2, and a jailer. One chair is electrified; the other is not. The
A mathematician attended a convention of fifty male and female scientists. The mathematician observed that if any two of them were picked at random, at least one of the two would be male. From this
Happy Harry wrapped up a present for his wife, and he put a gift inside a small box. He then put this box inside a second box, and then placed the second box inside a third. He completed his task by
Suppose a prisoner must make a choice between two doors. One door leads to freedom and the other door is booby-trapped so that it leads to death. The doors are labeled as follows:Door 1: This door
Sometimes statements p and q are described as contradictory, contrary, or inconsistent. Consult a logic text, and then define these terms using truth tables.
Consider the apparatus shown in Figure 3.9. Note that there are 12 chutes (numbered 1 to 12), and a ball dropped into a chute will slide down the tube until it reaches an AND-gate or an OR-gate. If
This problem is similar to the previous taxicab problem, only instead of five taxi drivers we consider nine persons who play positions on a baseball team.Data from Previous problemFive cabbies have
Five cabbies have been called to pick up five fares at the Hilton Towers. On arrival, they find that their passengers are slightly intoxicated. Each man has a different first and last name, a
Consider the following question: “Of all possible collections of states that yield 270 or more electoral votes—enough to win a presidential election—which collection has the smallest
Write a symbolic statement for each of the following verbal statements.a. Either Donna does not like Elmer because Elmer is bald, or Donna likes Frank and George because they are handsome
State and prove the principle of direct reasoning.
When will the light be on for a parallel circuit?
When will the light be on for a series circuit?
Explain when the light on a circuit is on and when it is off.
Design a circuit that will find the truth values for (p ∨ q) ∧ q.
Design a circuit for ∼p ∧ (∼q) . Show both the circuit and the simplified gate diagram.
The game of basketballa. If a player travels, then the other team gets possession of the ball.b. ball c. traveling d. baskete. free throwFor each of the situations in Problems 1–8, classify each
The game of Clue®a. The pack of cards consists of three groups: Suspects,Rooms, and Weapons. axiomb. Roll the die and move your token the number of squaresyou rolled. axiomc. a die undefined termd.
The game of Clue®a. playing board undefined termb. Professor Plum undefined termc. detective notebookd. You may not enter or land on a square that’s alreadyoccupied by another suspect. axiome.
The game of Sorry®a. pawn undefined termb. You take turns drawing cards from a special deck and moving your pawn around the board.c. home defined termd. Pawns may move forward or
The game of Monopoly®a. playing boardb. If you pass “GO,” then collect $200. c. passing “GO” d. “chance” carde. race car playing pieceFor each of the situations in Problems 1–8,
A man I know once owned a number of turkeys. One day, one of his gobblers flew over the man’s fence and laid an egg on a neighbor’s property. To whom did the egg belong— to the man who owned
Emor D. Nilap, a news reporter who was a little backward, was sent to cover a billiards tournament. Since he wanted to do a good job, he rounded up some human-interest facts to make his story a
During an ancient war, three prisoners were brought into a room. In the room was a large box containing three white hats and two black hats. Each man was blindfolded, and one of the hats was placed
On the South Side, a member of the mob had just knocked off a store.Since the boss had told them all to lay low, he was a bit mad. He decided to have a talk with the boys. It was Bogie or Clyde. Both
Consider the “letter game” patterned after an article by Don Gernes from Ponderosa High School. We have three undefined terms, the letters M, I, and U, and one definition, “x means any string
a.b.Determine whether each argument in Problems 5–8 is valid or invalid. Give reasons for your answer. P~q q -~P
a.b.Determine whether each argument in Problems 5–8 is valid or invalid. Give reasons for your answer. b.: d~ b A d
a.b.Determine whether each argument in Problems 5–8 is valid or invalid. Give reasons for your answer. Pq ~q ::~P
What is a syllogism?
What do we mean by logical fallacies?
a. Explain what we mean by direct reasoning.b. Explain what we mean by indirect reasoning.c. Explain what we mean by transitive reasoning.
Show that the following argument is not valid.If a person reads the Times, then she is well informed.This person is well informed.Therefore, this person reads the Times.
Form a valid conclusion using all the statements.1. All unripe fruit is unwholesome.2. All these apples are wholesome.3. No fruit grown in the shade is ripe.
Form a valid conclusion using all these statements. We number the premises for easy reference.1. If I receive a check for $500, then we will go on vacation.2. If the car breaks down, then we will not
(p ∧ q) ∨ (p → ∼q)Use truth tables in Problems 7–14 to determine whether the given compound statement is a tautology.
a. How long can you legally park if you arrive at 5:00 p.m.?b. How long can you legally park if you arrive at 4:00 p.m.?Use the parking signs in this photograph to answer the questions in Problems
a. How long can you legally park if you arrive at midnight?b. How long can you legally park if you arrive at 2:00 p.m.?Use the parking signs in this photograph to answer the questions in Problems
Discuss when you use the symbols → and ⇒.
Discuss when you use the symbols ↔ and ⇔.
Discuss the procedure for finding the negation of compound statements.
Show that (p→q) ⇔ ∼ (p ∧ ∼q).
Write the negation of the compound statements.a. John went to work or he went to bed.b. Alfie didn’t come last night and didn’t pick up his money.
The officer said to the detective, “If John was at the scene of the crime, then he knows that Jean could not have done it.” “No, Columbo,” answered the detective, “that is not correct. John
Show that the statement “p because q” as defined in Table 3.9 is equivalent to conjunction.Table 3.9 p q TT TF FT F F Either por q (pvq)^~(p^q) F T T LL Neither p nor q p unless q a p ~(pv q) F T
In Problems 25–30, first estimate your answer and then calculate the exact answer.It has been estimated that there are 107 billion pieces of mail per year. If the postage rates are raised 2¢, how
In Problems 25–30, first estimate your answer and then calculate the exact answer.In the musical Rent, there is a song called “Seasons of Love” that uses the number 525,600 minutes. How long is
In Problems 25–30, first estimate your answer and then calculate the exact answer.If your car gets 23 miles per gallon, how far can you go on 15 gallons of gas?
In Problems 25–30, first estimate your answer and then calculate the exact answer.If your car travels 280 miles and uses 10.2 gallons, how many miles per gallon did you get?
In Problems 25–30, first estimate your answer and then calculate the exact answer.If you are paid $16.25 per hour, what is your annual salary?
In Problems 25–30, first estimate your answer and then calculate the exact answer.How many pages are necessary to make 1,850 copies of a manuscript that is 487 pages long? (Print on one side only.)
Show the calculator steps for 14 + 38.
Perform the operations in Problems 7–18.a. 14 + 6 × 3b. 30 / 5 × 2
Perform the operations in Problems 7–18.a. 3 × 8 + 3 × 7b. 3(8 + 7)
Perform the operations in Problems 7–18.a. (8 + 6) / 2b. 8 + 6 / 2
Perform the operations in Problems 7–18.a. 12 + 6/3b. (12 + 6)/3
Perform the operations in Problems 7–18.a. 450 + 550 / 10b. 450 + 550 /10
Perform the operations in Problems 7–18.a. 20/2·5b. 20/(2·5)
Perform the operations in Problems 7–18.a. 10 + 5 x 2 + 6 × 3b. 4 + 3 x 8 + 6 + 4 × 5
Perform the operations in Problems 7–18.a. 8 + 2(3 + 12) - 5 x 3b. 25 - 4(12 - 2 x 6) + 3
Perform the operations in Problems 7–18.a. 3 + 9 / 3 x 2 +2 x 6 / 3b. [(3 + 9) / 3] x 2 + [(2 x 6) /3]
Find the eight pattern.Understand the Problem. What do we mean by the eight pattern? Do you understand the example for the nine pattern?
~r ∨ ~sConstruct a truth table for the statements given in Problems 5–22.
~(p ∧ q)Construct a truth table for the statements given in Problems 5–22.
~p ∧ ~qConstruct a truth table for the statements given in Problems 5–22.
~p ∨ qConstruct a truth table for the statements given in Problems 5–22.
What is the law of contraposition?
What is the law of double negation?
What is a truth table?
Assume that the following statement is true:p → ∼q If you obey the law, then you will not go to jail.Write the converse, inverse, and contrapositive.
Write the converse, inverse, and contrapositive of the statement:If it is a 380Z, then it is a car.
Make up an example illustrating each of the four cases for the conditional.
Construct a truth table to determine when the following statement is true. [bv (b / d)] V (bv d) ~
Use the law of double negation to rewrite the following statement made by an Iraqi official and reported on a national news report: “All that the U.S. has said about Iraq is a false lie.”
Construct a truth table for ∼(∼p) .
According to the definition, which of the examples in Problems 5–8 are statements?a. Dan and Mary were married on August 3, 1979.b. 6 + 12 ≠ 10 + 8c. Do not read this sentence.d. Do you have a
According to the definition, which of the examples in Problems 5–8 are statements?a. 6 + 9 ≠ 7 + 8b. Thomas Jefferson was the 23rd president.c. Sit down and be quiet!d. If wages continue to
According to the definition, which of the examples in Problems 5–8 are statements?a. March 18, 2011, is a Friday.b. Division by zero is impossible.c. Logic is difficult.d. 4 – 6 = 2
What do we mean by negation? Include as part of your answer the definition.

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