write the resulting set using the listing method. {-3, -1} ∩ {1, 3}
> Indicate true (T) or false (F). 1 ∊ {10, 11}
> Indicate true (T) or false (F). {3, 2, 1} ⊂ {1, 2, 3, 4}
> Use the given interest rate i per compounding period to find r, the annual rate. 0.47% per month
> Answer yes or no. (If necessary, review Section A.1). If the universal set is the set of integers, is the set of even integers the complement of the set of odd integers?
> Answer yes or no. (If necessary, review Section A.1). Is the set of integers the union of the set of even integers and the set of odd integers?
> Answer yes or no. (If necessary, review Section A.1). Is the set of rational numbers a subset of the set of integers?
> Use the Venn diagram to indicate which of the eight blood types are included in each set. Rh′ ∩ A
> Use the Venn diagram to indicate which of the eight blood types are included in each set. (A ∪ B ∪ Rh)′
> Use the Venn diagram to indicate which of the eight blood types are included in each set. A ∪ B
> Use the Venn diagram to indicate which of the eight blood types are included in each set. A ∩ B
> Voting coalition. The company’s leaders in Problem 89 decide for or against certain measures as follows: The president has 2 votes and each vice-president has 1 vote. Three favorable votes are needed to pass a measure. List all minimal winning coalitions
> Find the indicated number of elements by referring to the following table of enrollments in a finite mathematics class: Let the universal set U be the set of all 120 students in the class, A the set of students from the College of Arts & Sciences, B
> Find the indicated number of elements by referring to the following table of enrollments in a finite mathematics class: Let the universal set U be the set of all 120 students in the class, A the set of students from the College of Arts & Sciences, B
> Use formula (2) for the amount to find each of the indicated quantities. A = $6,608; r = 24%; t = 3 quarters; P = ?
> Find the indicated number of elements by referring to the following table of enrollments in a finite mathematics class: Let the universal set U be the set of all 120 students in the class, A the set of students from the College of Arts & Sciences, B
> Find the indicated number of elements by referring to the following table of enrollments in a finite mathematics class: Let the universal set U be the set of all 120 students in the class, A the set of students from the College of Arts & Sciences, B
> Find the indicated number of elements by referring to the following table of enrollments in a finite mathematics class: Let the universal set U be the set of all 120 students in the class, A the set of students from the College of Arts & Sciences, B
> Find the indicated number of elements by referring to the following table of enrollments in a finite mathematics class: Let the universal set U be the set of all 120 students in the class, A the set of students from the College of Arts & Sciences, B
> Find the indicated number of elements by referring to the following table of enrollments in a finite mathematics class: Let the universal set U be the set of all 120 students in the class, A the set of students from the College of Arts & Sciences, B
> Let A be a set that contains exactly n elements. Find a formula in terms of n for the number of subsets
> Discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counter example The empty set is a subset of the empty set.
> Discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counter example If A ⊂ B, then B′ ⊂ A′.
> Discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counter example If A = ∅, then A ∩ B = ∅.
> Discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counter example If A ∩ B = A, then A ⊂ B.
> Use the given interest rate i per compounding period to find r, the annual rate. 3.69% per half-year
> Discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counter example If A ⊂ B, then A ∪ B = A.
> Are the given sets disjoint? Let H, T, P, and E denote the sets in Problems 49, 50, 51, and 52, respectively. E and E
> Are the given sets disjoint? Let H, T, P, and E denote the sets in Problems 49, 50, 51, and 52, respectively. E and P
> Draw a Venn diagram for sets A, B, and C and shade the given region. (A ∩ B)′ ∪ C
> Draw a Venn diagram for sets A, B, and C and shade the given region. (A ∪ B)′
> Draw a Venn diagram for sets A, B, and C and shade the given region. A′ ∩ B′ ∩ C
> Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set. {2, 4, 6, 8, 10, … }
> Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set. {n ∈ N| n < 1000}
> For P, Q, and R in Problem 47, find P ∩(Q ∪ R). Data from Problem 47: For P = {1, 2, 3, 4}, Q = {2, 4, 6}, and R = {3, 4, 5,6 }, find P ∪ (Q ∩ R).
> If R = {1, 3, 4} and T = {2, 4, 6}, find (A) {x |x ∊ R and x ∊ T}
> Use formula (2) for the amount to find each of the indicated quantities. P = $3,000; r = 4.5%; t = 30 days; A = ?
> Refer to the Venn diagram below and find the indicated number of elements. n(A ∩ A′)
> Refer to the Venn diagram below and find the indicated number of elements. n(A′ ∩ B′)
> Refer to the Venn diagram below and find the indicated number of elements. n((A ∩ B)′)
> Refer to the Venn diagram below and find the indicated number of elements. n(A ∩ B′)
> Refer to the Venn diagram below and find the indicated number of elements. n(B′)
> Refer to the Venn diagram below and find the indicated number of elements. n(A ∩ B)
> Refer to the Venn diagram below and find the indicated number of elements. n(A)
> For U = {7, 8, 9, 10, 11} and A = {7, 11}, find A′.
> write the resulting set using the listing method. {x | x is a month starting with M}
> write the resulting set using the listing method. {x | x4 = 16}
> Use the given interest rate i per compounding period to find r, the annual rate. 0.012% per day
> write the resulting set using the listing method. {x | x2 = 36}
> write the resulting set using the listing method. {-3, -1,} ∪ {1, 3}
> write the resulting set using the listing method. {1, 2, 4} ∩{4, 8, 16}
> write the resulting set using the listing method. {1, 2, 4} ∪ {4, 8, 16}
> Indicate true (T) or false (F). ∅ ⊂ {1, 2, 3}
> Indicate true (T) or false (F). {0, 6} = {6}
> Explain why the product of any two odd integers is odd
> Refer to the footnote for the definitions of divisor, multiple, prime, even, and odd. List the primes between 10 and 20.
> Refer to the footnote for the definitions of divisor, multiple, prime, even, and odd. List the positive multiples of 9 that are less than 50
> Use formula (1) for simple interest to find each of the indicated quantities. I = $96; P = $3,200; r = 4%; t = ?
> Refer to the footnote for the definitions of divisor, multiple, prime, even, and odd. List the positive integers that are divisors of 24.
> Can a conditional proposition be false if its converse is true? Explain.
> If the conditional proposition p is a contradiction, is ¬p a contingency, a tautology, or a contradiction? Explain.
> Let p be the proposition “every politician is honest.” Explain why the statement “every politician is dishonest” is not equivalent to ¬p. Express ¬p as an English sentence without using the word not.
> verify each equivalence using formulas from Table 2. ¬(¬p → ¬q) ( q ( ¬p
> verify each equivalence using formulas from Table 2. ¬p → q ( p ( q
> construct a truth table to verify each equivalence. p → (p ( q) ( p → q
> construct a truth table to verify each equivalence. p ( (p → q) ( p ( q
> Construct a truth table to verify each equivalence. q → (¬p ( q) ( ¬(p ( q)
> Construct a truth table to verify each implication. (p ( ¬p) ( q
> Use the given interest rate i per compounding period to find r, the annual rate. 1.57% per quarter
> Evaluate the expression. If the answer is not an integer, round to four decimal places.
> construct a truth table to verify each implication. p ( q ( p → q
> construct a truth table to verify each implication. ¬p ( p → q
> Construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction. (p →¬q) ( (p ( q)
> Construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction. q → (p (¬ q)
> Construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction. ¬ p → (p ( q)
> Construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction. (p → q) → ¬q
> Construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction. p → (p ( q)
> Construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction. p ( (p → q)
> Construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction. q ( (p ( q)
> Construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction. p → ¬q
> Use formula (1) for simple interest to find each of the indicated quantities. I = $28; P = $700; t = 13 weeks; r = ?
> Construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction. p ( ¬ q
> State the converse and the contrapositive of the given proposition. If n is an integer that is a multiple of 6, then n is an integer that is a multiple of 2 and a multiple of 3.
> State the converse and the contrapositive of the given proposition. If g1x2 is a quadratic function, then g1x2 is a function that is neither increasing nor decreasing.
> State the converse and the contrapositive of the given proposition. If triangle ABC is isosceles, then the base angles of triangle ABC are congruent.
> Describe each proposition as a negation, disjunction, conjunction, or conditional, and determine whether the proposition is true or false. If 4 is even, then 4 is prime
> Describe each proposition as a negation, disjunction, conjunction, or conditional, and determine whether the proposition is true or false. 9 is even or 9 is prime
> Describe each proposition as a negation, disjunction, conjunction, or conditional, and determine whether the proposition is true or false. -3 is not greater than 0
> Describe each proposition as a negation, disjunction, conjunction, or conditional, and determine whether the proposition is true or false. -3 < 0 and -3 > 0
> Express each proposition as an English sentence and determine whether it is true or false, where r and s are the propositions The converse of s ( r
> Express each proposition as an English sentence and determine whether it is true or false, where r and s are the propositions ¬ r
> Use the given annual interest rate r and the compounding period to find i, the interest rate per compounding period. 10.95% compounded daily
> Express each proposition as an English sentence and determine whether it is true or false, where r and s are the propositions r ( s
> Express each proposition as an English sentence and determine whether it is true or false, where p and q are the propositions. p: “91 is prime” q: “91 is odd” The contrapositive of p → q
> Express each proposition as an English sentence and determine whether it is true or false, where p and q are the propositions. p: “91 is prime” q: “91 is odd” p → q
> Express each proposition as an English sentence and determine whether it is true or false, where p and q are the propositions. p: “91 is prime” q: “91 is odd” p v q
> (A) Introduce slack, surplus, and artificial variables and form the modified problem. (B) Write the preliminary simplex tableau for the modified problem and find the initial simplex tableau. (C) Find the optimal solution of the modified problem by appl
> (A) Introduce slack, surplus, and artificial variables and form the modified problem. (B) Write the preliminary simplex tableau for the modified problem and find the initial simplex tableau. (C) Find the optimal solution of the modified problem by appl
> (A) Introduce slack, surplus, and artificial variables and form the modified problem. (B) Write the preliminary simplex tableau for the modified problem and find the initial simplex tableau. (C) Find the optimal solution of the modified problem by appl
> (A) Introduce slack, surplus, and artificial variables and form the modified problem. (B) Write the preliminary simplex tableau for the modified problem and find the initial simplex tableau. (C) Find the optimal solution of the modified problem by appl
> Construct a mathematical model in the form of a linear programming problem. Do not solve. A farmer grows three crops: corn, oats, and soybeans. He mixes them to feed his cows and pigs. At least 40% of the feed mix for the cows must be corn. The feed mix
