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, …}
> 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)
> 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.
> 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)’
> In Exercises 39–50, use the Venn diagram in Fig. 2.24 to list the sets in roster form. A ( (B ( C)
> In Exercises 39–50, use the Venn diagram in Fig. 2.24 to list the sets in roster form. (A ( C)’
> Profit Margins The following chart shows retail stores’ average percent profit margin on certain items. (a) Determine the average profit of a store that has the list price of $620 on a camcorder. (b) Determine the average profit of a s
> In Exercises 39–50, use the Venn diagram in Fig. 2.24 to list the sets in roster form. A ( B ( C
> In Exercises 39–50, use the Venn diagram in Fig. 2.24 to list the sets in roster form. (B ( C)’
> In Exercises 39–50, use the Venn diagram in Fig. 2.24 to list the sets in roster form. A ( C
> 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. B’
> In Exercises 39–50, use the Venn diagram in Fig. 2.24 to list the sets in roster form. C
> In Exercises 39–50, use the Venn diagram in Fig. 2.24 to list the sets in roster form. U
> In Exercises 39–50, use the Venn diagram in Fig. 2.24 to list the sets in roster form. A
> Senate Bills In Exercises 33–38, use Fig. 2.23. During a session of the U.S. Senate, three bills were voted on. The votes of six senators are shown. Determine in which region of the figure each senator should be placed. The set labeled
> Senate Bills In Exercises 33–38, use Fig. 2.23. During a session of the U.S. Senate, three bills were voted on. The votes of six senators are shown. Determine in which region of the figure each senator should be placed. The set labeled
> Convert the given numeral to a numeral inbase 10. D20E16
> Senate Bills In Exercises 33–38, use Fig. 2.23. During a session of the U.S. Senate, three bills were voted on. The votes of six senators are shown. Determine in which region of the figure each senator should be placed. The set labeled
> Senate Bills In Exercises 33–38, use Fig. 2.23. During a session of the U.S. Senate, three bills were voted on. The votes of six senators are shown. Determine in which region of the figure each senator should be placed. The set labeled
> Senate Bills In Exercises 33–38, use Fig. 2.23. During a session of the U.S. Senate, three bills were voted on. The votes of six senators are shown. Determine in which region of the figure each senator should be placed. The set labeled
> Senate Bills In Exercises 33–38, use Fig. 2.23. During a session of the U.S. Senate, three bills were voted on. The votes of six senators are shown. Determine in which region of the figure each senator should be placed. The set labeled
> In Exercises 21–32, indicate in Fig. 2.22 the region in which each of the figures should be placed.
