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sciences
nature of mathematics

Questions and Answers of Nature Of Mathematics

Hannah will not watch Jon Stewart or she will watch the NBC late-night orchestra.Use the tautology (p → q) ⇔ (∼p ∨ q) to write each statement in Problems 29–34 in an equivalent form.
We will not visit New York or we will visit the Statue of Liberty.Use the tautology (p → q) ⇔ (∼p ∨ q) to write each statement in Problems 29–34 in an equivalent form.
I am obligated to pay the rent because I signed the contract.Translate the statements in Problems 19–28 into symbols. For each simple statement, indicate the meanings of the symbols you use.
Verify the indicated definition in Problems 15–18 from Table 3.9 using a truth table.p unless qTable 3.9 Either p or q pq (pvq)^~(p^q) TT F TF FT FF T T F Neither p nor q p unless q ~(p vq) ~q p F
Neither p nor qVerify the indicated definition in Problems 15–18 from Table 3.9 using a truth table.Table 3.9 Either p or q pq (pvq)^~(p^q) TT F TF FT FF T T F Neither p nor q p unless q ~(pvq) ~q
Either p or qVerify the indicated definition in Problems 15–18 from Table 3.9 using a truth table.Table 3.9 Either p or q pq (pvq)^~(p^q) TT F TF FT FF T T F Neither p nor q p unless q ~q p ~(pvq)
Use truth tables in Problems 7–14 to determine whether the given compound statement is a tautology.(p ∨ ∼q) ↔ (~p ∨ q)
Use truth tables in Problems 7–14 to determine whether the given compound statement is a tautology.(p ∨ q) ↔ (q ∨ p)
Use truth tables in Problems 7–14 to determine whether the given compound statement is a tautology.(p ∧ q) ↔ (p ∨ q)
Use truth tables in Problems 7–14 to determine whether the given compound statement is a tautology.(∼q →p) →q
Use truth tables in Problems 7–14 to determine whether the given compound statement is a tautology.(∼p → q) →p
Use truth tables in Problems 7–14 to determine whether the given compound statement is a tautology.(p ∨ q) ∧ (q → ∼p)
Discuss the difference between the conditional and the biconditional.
Rewrite the following as one statement:1. If a polygon has three sides, then it is a triangle.2. If a polygon is a triangle, then it has three sides.
Is (p ∨ q) → (∼q →p) a tautology?
Perform the operations in Problems 7–18.a. 1 + 3 x 2+4+3 x 6b. 3 + 6 x 2+8+4 x 3
Perform the operations in Problems 7–18.a. 3 + [(9 / 3) × 2] + [(2 × 6) / 3]b. [(3 + 9) / (3 × 2] + [(2 × 6) / 3]
Perform the operations in Problems 7–18.a. 5 + 2 × 6b. 7 + 3 × 2
Decide about the truth or falsity of the following statement:If wishes were horses, then beggars could ride.
Decide about the truth or falsity of the following statement:If Apollo can do anything, could he make an object that he could not lift?
Utilities, except for water and garbage, are paid by the tenant. Let t: You are a tenant.w: You pay water.g: You pay garbage.u: You pay the other utilities.t→In Problems 53–58, fill in the blanks
The tenant agrees to lease the premises for 12 months beginning on September 1 and at a monthly rental charge of $800. Let t: You are a tenant.m: You lease the premises for 12 months.s: You will
This contract is noncancellable by tenant for 60 days. Let t: You are a tenant.d: It is within 60 days.c: This contract can be canceled.(t ∧ d) →___________In Problems 53–58, fill in the blanks
To qualify for the special fare, you must fly on Monday, Tuesday, Wednesday, or Thursday, and you must stay over a Saturday evening. Letq: You qualify for the special fare.m: You fly on Monday.t: You
To qualify for a loan, the applicant must have a gross income of at least $35,000 if single or combined income of $50,000 if married. Letq: You qualify for a loan.m: You are married.i: You have an
The applicant for the position must have a two-year college degree in drafting or five years of experience in the field.Assume these are the only requirements for the position. Let a: You are an
If the income on line 1 was reported to you on Form W-2 and the “Statutory employee” box on that form was checked, see instructions for line 1 (Schedule C) and check here.Translate the statements
If you are a student or disabled, see line 6 of instructions.Translate the statements in Problems 47–52 into symbolic form.
If married and filing a joint return, enter your spouse’s earned income.Translate the statements in Problems 47–52 into symbolic form.
If line 32 is $86,025 or less, multiply $2,500 by the total number of exemptions claimed on line 6e.Translate the statements in Problems 47–52 into symbolic form.
If the amount on line 31 is less than $26,673 and a child lives with you, turn to page 27.Translate the statements in Problems 47–52 into symbolic form.
If the qualifying person is a child and not your dependent, enter this child’s name.Translate the statements in Problems 47–52 into symbolic form.
Let p: 1 + 1 = 2; q: 9 – 3 = 5.a. (p → ∼q) →(q → ∼p)b. (p →q) → (∼q → ∼p)Tell which of the statements in Problems 43–46 are true.
Let p: 5 + 8 = 10; q: 4 + 4 = 8.a. (p ∧ ∼q) ∧ pb. p ∨ (p →q)c. (p ∧ q) →p)Tell which of the statements in Problems 43–46 are true.
Let p: 2 is prime; q: 1 is prime.a. ~p ∨ ~qb. ~ (~p)c. (p ∧ q) ∨ ~qTell which of the statements in Problems 43–46 are true.
Let p: 2 + 3 = 5; q: 12 – 7 = 5.a. ~p ∨ qb. ~p ∧ ~qc. ~ (p ∧ q)Tell which of the statements in Problems 43–46 are true.
3 · 2 = 6 only if water runs uphill.First, decide whether each simple statement in Problems 39–42 is true or false. Then state whether the given compound statement is true or false.
If 1 + 1 = 10, then the moon is made of green cheese.First, decide whether each simple statement in Problems 39–42 is true or false. Then state whether the given compound statement is true or false.
The moon is made of green cheese only if Mickey Mouse ispresident.First, decide whether each simple statement in Problems 39–42 is true or false. Then state whether the given compound statement is
If 5 + 10 = 16, then 15 - 10 = 3.First, decide whether each simple statement in Problems 39–42 is true or false. Then state whether the given compound statement is true or false.
Everything’s got a moral if only you can find it. (Lewis Carroll)Translate the sentences in Problems 31–38 into if-then form.
All work is noble. (Thomas Carlyle)Translate the sentences in Problems 31–38 into if-then form.
All useless life is an early death. (Goethe)Translate the sentences in Problems 31–38 into if-then form.
We are not weak if we make a proper use of those meanswhich the God of Nature has placed in our power. (PatrickHenry)Translate the sentences in Problems 31–38 into if-then form.
Everything happens to everybody sooner or later if there is time enough. (G. B. Shaw)Translate the sentences in Problems 31–38 into if-then form.
Repeat Example 6, except this time assume that you do not have charitable contributions, but all other statements are true.Data from Example 6The following sentence is found on a tax form:If you do
[p ∧ (q ∨ ~p)] ∨ rConstruct a truth table for the statements given in Problems 5–22.
[(p ∨ q) ∧ ~r] ∧ rConstruct a truth table for the statements given in Problems 5–22.
[p ∨ (p ∧ q)] →pConstruct a truth table for the statements given in Problems 5–22.
Construct a truth table for the statements given in Problems 5–22.[p ∧ (p ∨ q)] →p
(~p ∧ q) ∨ ~qConstruct a truth table for the statements given in Problems 5–22.
Construct 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 ∧ ∼q
Construct a truth table for the statements given in Problems 5–22.~(~r)
What is a conditional? Discuss.
Construct a truth table for the compound statement:Alfie did not come last night and did not pick up his money.
Their are three errers in this item. See if you can find all three.
Smith received the following note from Melissa: “Dr. Smith, I wish to explain that I was really joking when I told you that I didn’t mean what I said about reconsidering my decision not to change
Prove the law of double negation. That is, prove that for any statement p, ∼(∼p) has the same truth value as p.
In Problems 50–57, find the truth value when p is T, q is F, and r is F. (q V~g) ^ [(p^~q) V (~r Vr)]
In Problems 50–57, find the truth value when p is T, q is F, and r is F. (p/q) V [(p V ~q) V (~r/p)]
In Problems 50–57, find the truth value when p is T, q is F, and r is F. ~(r^g) ^ (q V ~q)
In Problems 50–57, find the truth value when p is T, q is F, and r is F. ~(~p) ^ (qV p)
In Problems 50–57, find the truth value when p is T, q is F, and r is F. (p^~q) V (r^ ~q)
In Problems 50–57, find the truth value when p is T, q is F, and r is F. (pVq) ~(p V ~q) A
In Problems 50–57, find the truth value when p is T, q is F, and r is F. PV (q^r)
In Problems 50–57, find the truth value when p is T, q is F, and r is F. (p ^ g) & r
a. Marsha finished the sign and table, or a pair of chairs.b. Marsha finished the sign, and the table or a pair of chairs.Translate the word statements in Problems 41–49 into symbolic form, using
a. Dinner includes soup and salad, or the vegetable of the day.b. Dinner includes soup, and salad or the vegetable of the day.Translate the word statements in Problems 41–49 into symbolic form,
The winner must have an A.A. degree in drafting or three years of professional experience.Translate the word statements in Problems 41–49 into symbolic form, using only simple statements as
The successful applicant for the job will have a B.A. degree in liberal arts or psychology.Translate the word statements in Problems 41–49 into symbolic form, using only simple statements as
The decision will depend on judgment or intuition, and not on who paid the most.Translate the word statements in Problems 41–49 into symbolic form, using only simple statements as variables. Be
Fat Albert lives to eat and does not eat to live.Translate the word statements in Problems 41–49 into symbolic form, using only simple statements as variables. Be sure to indicate the meanings of
Jack will not go tonight, and Rosamond will not go tomorrow.Translate the word statements in Problems 41–49 into symbolic form, using only simple statements as variables. Be sure to indicate the
Sam will not seek and will not accept the nomination.Translate the word statements in Problems 41–49 into symbolic form, using only simple statements as variables. Be sure to indicate the meanings
W. C. Fields is eating, drinking, and having a good time.Translate the word statements in Problems 41–49 into symbolic form, using only simple statements as variables. Be sure to indicate the
Assume p is T, q is F, and r is T.Find the truth value for each of the compound statements inProblems 35–40. a. (p^q) V (p^ ~r)
Assume p is T, q is T, and r is T.Find the truth value for each of the compound statements in Problems 35–40. a. (pVg) (r^~q)
Assume p is T, q is T, and r is T.Find the truth value for each of the compound statements in Problems 35–40. a. p^ (qVr)
Assume p is T, q is T, and r is F.Find the truth value for each of the compound statements in Problems 35–40. a. (pVq) Ar
Assume r is T, s is T, and t is T.Find the truth value for each of the compound statements in Problems 35–40. a. r^ (st)
Assume r is F, s is T, and t is T.Find the truth value for each of the compound statements in Problems 35–40. a. (r Vs) Vt
Assume p is T and q is T. Under these assumptions, which of the statements in Problem 31 are true?Data from problem 31Let p: Prices will rise; q: Taxes will rise. Translate each of the following
Use Figure 3.2 to decide whether each of the statements in Problems 15–19 is true or false.Figure 3.2No 21st-century president has white hair. Harry S. Truman (Democrat) 1945-1953 Hulton
Use Figure 3.2 to decide whether each of the statements in Problems 15–19 is true or false.Figure 3.2At least one president parts his hair. Harry S. Truman (Democrat) 1945-1953 Hulton Archive/Getty
Use Figure 3.2 to decide whether each of the statements in Problems 15–19 is true or false.Figure 3.2All are either Democrat or Republican. Harry S. Truman (Democrat) 1945-1953 Hulton Archive/Getty
Answer the questions in Problems 9–14 about the presidents shown in Figure 3.2.Figure 3.2Who is a 20th-century president and a Democrat? Harry S. Truman (Democrat) 1945-1953 Hulton Archive/Getty
Answer the questions in Problems 9–14 about the presidents shown in Figure 3.2.Figure 3.2Who is a 19th-century president with a mustache? Harry S. Truman (Democrat) 1945-1953 Hulton Archive/Getty
Answer the questions in Problems 9–14 about the presidents shown in Figure 3.2.Figure 3.2Who has sideburns and a beard? Harry S. Truman (Democrat) 1945-1953 Hulton Archive/Getty Images Barack Obama
Answer the questions in Problems 9–14 about the presidents shown in Figure 3.2.Figure 3.2Who has glasses and no mustache? Harry S. Truman (Democrat) 1945-1953 Hulton Archive/Getty Images Barack
All infinite sets are uncountable.Determine whether each statement in Problems 55–58 is true or false. Give reasons for your answers.
Determine whether each statement in Problems 55–58 is true or false. Give reasons for your answers.All uncountable sets are infinite.
{2, 4, 8, 16, 32, . . .}An infinite set is said to be countably infinite if it can be placed into a one-to-one correspondence with the set of counting numbers, N. If the set cannot be placed into
Set of realsAn infinite set is said to be countably infinite if it can be placed into a one-to-one correspondence with the set of counting numbers, N. If the set cannot be placed into such a
Set of rationalsAn infinite set is said to be countably infinite if it can be placed into a one-to-one correspondence with the set of counting numbers, N. If the set cannot be placed into such a
Set of integersAn infinite set is said to be countably infinite if it can be placed into a one-to-one correspondence with the set of counting numbers, N. If the set cannot be placed into such a
Set of whole numbersAn infinite set is said to be countably infinite if it can be placed into a one-to-one correspondence with the set of counting numbers, N. If the set cannot be placed into such a
{4, 44, 444, 4444, . . .}Show that each set in Problems 45–48 is infinite by placing it into a one-to-one correspondence with a proper subset of itself.
{12, 14, 16, . . .}Show that each set in Problems 45–48 is infinite by placing it into a one-to-one correspondence with a proper subset of itself.
Show that each set in Problems 45–48 is infinite by placing it into a one-to-one correspondence with a proper subset of itself. N

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