Construct a truth table for the statement. ( p ( ( q
> In Exercises 23–26, show that the set has cardinality / by establishing a one-to-one correspondence between the set of counting numbers and the given set. {1, 4, 9, 16, 25, p }
> If p is true, q is false, and r is false, find the truth value of the statement. ( [ p ( (q ( r)]
> If p is true, q is false, and r is false, find the truth value of the statement. ((p ((q) ( ( r
> If p is true, q is false, and r is false, find the truth value of the statement. r ( (( p ( ( q)
> If p is true, q is false, and r is false, find the truth value of the statement. (p ( q) ( (q ( ( r )
> If p is true, q is false, and r is false, find the truth value of the statement. ( p ( ( q) ( ( r
> If p is true, q is false, and r is false, find the truth value of the statement. p ( (q (r)
> Convert each of the following to a numeral in the base indicated. 1098 to base 8
> Determine whether the statement is an implication. [( p ( q) ( r] ( ( p ( q)
> Determine whether the statement is an implication. [( p (q) ( (q ( p)] (( p ( q)
> Determine whether the statement is an implication. ( p ( q) ( ( p ( ,r)
> In Exercises 13–22, show that the set has cardinal number / by establishing a one-to-one correspondence between the set of counting numbers and the given set. Be sure to show the pairing of the general terms in the sets.
> Determine whether the statement is an implication. (p ( ( ( p ( q)
> Determine whether the statement is an implication. p ( ( p ( q)
> Determine whether the statement is an implication. ( p ( p
> Determine whether the statement is a tautology, self-contradiction, or neither. (( p ( q) ( (p ( ( q)
> Determine whether the statement is a tautology, self-contradiction, or neither. (,q ( p) ( ( q
> Determine whether the statement is a tautology, self-contradiction, or neither. (p (( q) 4 ((p ( q)
> Determine whether the statement is a tautology, self-contradiction, or neither. (p ( (q ( ( q)
> Investing You place $1000 in a mutual fund. The first year, the value of the fund increases by 10%. The second year, the value of the fund decreases by 10%. Determine the value of the fund at the end of the second year. Is it greater than, less than, or
> Determine whether the statement is a tautology, self-contradiction, or neither. ((p ( q) ( (q
> Determine whether the statement is a tautology, self-contradiction, or neither. (p ( q) (( q
> In Exercises 13–22, show that the set has cardinal number / by establishing a one-to-one correspondence between the set of counting numbers and the given set. Be sure to show the pairing of the general terms in the sets.
> Write the statement in symbolic form. Then construct a truth table for the symbolic statement. It is false that if Elaine went to lunch, then she cannot take a message and we will have to go home.
> Write the statement in symbolic form. Then construct a truth table for the symbolic statement. If it is not too cold then we can take a walk, or we can go to the gym.
> Write the statement in symbolic form. Then construct a truth table for the symbolic statement. If the dam holds then we can go fishing, if and only if the pole is not broken.
> Write the statement in symbolic form. Then construct a truth table for the symbolic statement. The election was fair if and only if the polling station stayed open until 8 p.m., or we will request a recount
> Write the statement in symbolic form. Then construct a truth table for the symbolic statement. We will advance in the tournament if and only if Max plays, or Pondo does not show up.
> Write the statement in symbolic form. Then construct a truth table for the symbolic statement. If today is Monday, then the library is open and we can study together.
> Construct a truth table for the statement. ((p ( (q) ( ((q ( r)
> Construct a truth table for the statement. ( p ( q) ( ((q ( (r)
> Convert each of the following to a numeral in the base indicated. 549 to base 7
> In Exercises 3–12, show that the set is infinite by placing it in a one-to-one correspondence with a proper subset of itself. Be sure to show the pairing of the general terms in the sets. { 2, 3, 4, 5, 6, …}
> In Exercises 13–22, show that the set has cardinal number / by establishing a one-to-one correspondence between the set of counting numbers and the given set. Be sure to show the pairing of the general terms in the sets.
> Construct a truth table for the statement. [r ( (q ( ( p)] ( (p
> Construct a truth table for the statement. (( r ( (q) ( p
> Construct a truth table for the statement. ( p ( r) ( (q ( r)
> Construct a truth table for the statement. (p ( (q ( (r)
> Construct a truth table for the statement. ((p ( q) ( r
> Construct a truth table for the statement. (p((q ( r)
> Construct a truth table for the statement. ( p ( q) ( ( p ( q)
> construct a truth table for the statement. ( ( p ( ( q)
> Construct a truth table for the statement. ((q ( p) ( ( q
> Construct a truth table for the statement. p ( (q ( p)
> In Exercises 13–22, show that the set has cardinal number / by establishing a one-to-one correspondence between the set of counting numbers and the given set. Be sure to show the pairing of the general terms in the sets.
> Adjusting for Inflation Assume that the rate of inflation is 2% per year for the next 2 years. What will the price of a sofa be 2 years from now if the sofa costs $999 today?
> Construct a truth table for the statement. ( p ( q)(p
> Construct a truth table for the statement. (p ( q) ( p
> Construct a truth table for the statement. ((p ( q)
> In Exercises 7–16, construct a truth table for the statement. (p ( (q
> Construct a truth table for the statement. (( p ( ( q )
> Construct a truth table for the statement. (p ( ( q
> Construct a truth table for the statement. p ( ( q
> Construct a truth table for the statement. q ( ( p
> In Exercises 13–22, show that the set has cardinal number / by establishing a one-to-one correspondence between the set of counting numbers and the given set. Be sure to show the pairing of the general terms in the sets. {7, 11, 15, 19, 23, p }
> Construct a truth table for the statement. p ( ( p
> Convert each of the following to a numeral in the base indicated. 102 to base 5
> Construct a truth table for the statement. p ( ( p
> Must ( p ( ( q ) ( r and ( q ( ( r ) ( p have the same number of trues in their answer columns? Explain.
> 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 statements p, q, r, and s have? b) List all possible true–f
> Construct a truth table for the symbolic statement. [ ( q ( ( r ) ( ( ( p ( ( q ) ] ( ( p ( ( r )
> Construct a truth table for the symbolic statement. ( [ ( ( ( p ( q ) ) ( ( q ( r) ]
> Airline Special Fares An airline advertisement states, “To get the special fare you must purchase your tickets between January 1 and February 15 and fly round trip between March 1 and April 1. You must depart on a Monday, Tuesday, or
> Read the requirements and each applicant’s qualifications for obtaining a loan. (a) Identify which of the applicants would qualify for the loan. (b) For the applicants who do not qualify for the loan, explain why. To qualify for a loan of $45,000, an ap
> Read the requirements and each applicant’s qualifications for obtaining a loan. (a) Identify which of the applicants would qualify for the loan. (b) For the applicants who do not qualify for the loan, explain why. To qualify for a loan of $40,000, an app
> In Exercises 13–22, show that the set has cardinal number / by establishing a one-to-one correspondence between the set of counting numbers and the given set. Be sure to show the pairing of the general terms in the sets. {2, 5, 8, 11, 14, p }
> In Exercises 3–12, show that the set is infinite by placing it in a one-to-one correspondence with a proper subset of itself. Be sure to show the pairing of the general terms in the sets.
> In Exercises 3–12, show that the set is infinite by placing it in a one-to-one correspondence with a proper subset of itself. Be sure to show the pairing of the general terms in the sets. {5, 7, 9, 11, 13, …}
> Construct a Venn diagram illustrating the following sets. U = {a, b, c, d, e, f, g, h, i, j} A = {c, d, e, g, h, i} B = {a, c, d, g} C = {c, f, i, j}
> Convert each of the following to a numeral in the base indicated. 11 to base 2
> Construct a Venn diagram illustrating the following sets. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {3, 4, 6, 7, 8, 9} B = {1, 3, 4, 8} C = {3, 5, 6, 10}
> A Venn diagram contains three sets, A, B, and C, as in Fig. 2.15 on page 66. If region V contains 4 elements and there are 9 elements in A y B, how many elements belong in region II? Explain.
> A Venn diagram contains three sets, A, B, and C, as in Fig. 2.15 on page 66. If region V contains 4 elements and there are 12 elements in B ( C, how many elements belong in region VI? Explain.
> (a) Construct a Venn diagram illustrating four sets, A, B,C, and D. (Hint: Four circles cannot be used, and you should end up with 16 distinct regions.) Have fun! (b) Label each region with a set statement (see Exercise 72). Check all 16 regions to make
> We were able to determine the number of elements in the union of two sets with the formula n(A ( B) = n(A) + n(B) – n(A ( B). Can you determine a formula for finding the number of elements in the union of three sets? In other words, write a formula to de
> Categorizing Contracts J & C Mechanical Contractors wants to classify its projects. The contractors categorize set A as construction projects, set B as plumbing projects, and set C as projects with a budget greater than $300,000. (a) Draw a Venn diagram
> Define each of the eight regions in Fig. 2.25 using sets A, B, and C and a set operation. (Hint: A y B9 y C9 defines region I.)
> Blood Types A hematology text gives the following information on percentages of the different types of blood worldwide. Construct a Venn diagram similar to the one in Example 2 and place the correct percentage in each of the eight regions.
> In Exercises 65–68, use a set statement to write a description of the shaded area. Use union, intersection, and complement as necessary. More than one answer may be possible
> In Exercises 65–68, use a set statement to write a description of the shaded area. Use union, intersection, and complement as necessary. More than one answer may be possible
> Income Taxes The federal income tax rate schedule for a joint return in 2014 is illustrated in the table below. If the Marquez family paid $12,715 in federal taxes, determine the family’s adjusted gross income.
> In Exercises 65–68, use a set statement to write a description of the shaded area. Use union, intersection, and complement as necessary. More than one answer may be possible
> In Exercises 65–68, use a set statement to write a description of the shaded area. Use union, intersection, and complement as necessary. More than one answer may be possible
> In Exercises 57–64, use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.
> In Exercises 57–64, use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.
> In Exercises 57–64, use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.
> In Exercises 57–64, use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.
> In Exercises 57–64, use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.
> In Exercises 57–64, use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.
> In Exercises 57–64, use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.
> In Exercises 57–64, use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.
> Convert each of the following to a numeral in the base indicated. 7 to base 2
> In Exercises 51–56, use Venn diagrams to determine whether the following statements are equal for all sets A and B.
> In Exercises 51–56, use Venn diagrams to determine whether the following statements are equal for all sets A and B.
> In Exercises 51–56, use Venn diagrams to determine whether the following statements are equal for all sets A and B.
> In Exercises 51–56, use Venn diagrams to determine whether the following statements are equal for all sets A and B.
> In Exercises 51–56, use Venn diagrams to determine whether the following statements are equal for all sets A and B.
> In Exercises 51–56, use Venn diagrams to determine whether the following statements are equal for all sets A and B.
> In Exercises 39–50, use the Venn diagram in Fig. 2.24 to list the sets in roster form. A’ – B
> In Exercises 39–50, use the Venn diagram in Fig. 2.24 to list the sets in roster form. (A - B)’
