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All Textbook Solutions for Mathematical Excursions (MindTap Course List)
67RE68RE69RE70RE71RE72RE1T2T3T4T5T6T7T8T9T10T11T12T13T14TUpgrade Options An automobile company makes a sedan with nine upgrade options. a. How many different versions of this sedan can the company produce? b. What is the minimum number of upgrade options the company must provide if it wishes to offer at least 2500 versions of this sedan?Student Demographics A college finds that 841 of its students are receiving financial aid, 525 students are business majors, and 202 students are receiving financial aid and are business majors. How many students are receiving financial aid or are business majors?The following bar graph shows the monthly principal and interest payment needed to purchase an average-priced existing home in the United States from 2007 to 2014. Use the information in the bar graph and the roster method to represent each of the following sets. a. The set of years in which the monthly principal and interest payment was greater than $800. b. The set of months in which the monthly principal and interest payment was greater than $700 but less than $900. C. The set of months in which the monthly principal and interest payment was less than $600.A survey of 1000 households was taken to determine how they obtained news about current events. The survey considered only television. Newspapers, and the Internet as sources for news. Of the households surveyed, 724 obtained news from television. 545 obtained news from newspapers. 280 obtained news from the Internet. 412 obtained news from both television and newspapers. 185 obtained news from both television and the Internet. 105 obtained news from television, newspapers, and the Internet. 64 obtained news from the Internet but not from television or newspapers. Of those households that were surveyed, a. how many obtained news from television hut not from newspapers or the Internet? b. how many obtained news from newspapers but not from television or the Internet? c. how many obtained news from television or newspapers? d. how many did not acquire news from television, newspapers, or the Internet?Show a method that can be used to establish a one-to-one correspondence between the elements of the following sets. {5,10, 15,20,25,...,5n,...},W20TWrite a symbolic statement to represent each of the networks.Write a symbolic statement to represent each of the networks.Write a symbolic statement to represent each of the networks.Write a symbolic statement to represent each of the networks.Write a symbolic statement to represent each of the networks.Write a symbolic statement to represent each of the networks.Which of the networks in Excursion Exercises 1 to 6 are closed networks, given that P is closed, Q is open. R is closed, and S is open?Which of the networks in Excursion Exercises I to 6 are closed networks, given that P is open, Q is closed, R is closed, and S is closed?Draw a network to represent each statement. (PQ)(RP)Draw a network to represent each statement. P[ (QR)R ]Draw a network to represent each statement. [ PQR ](PR)Draw a network to represent each statement. (QR)(SP)Draw a network to represent each statement. [ (PR)Q ](R)14EEWarning Circuits The circuits shown in Excursion Exercises 15 and 16 include a switching network, a warning Light, and a battery. In each circuit the warning light will turn on only when the switching network is closed. Consider the following circuit. For each of the following conditions, determine whether the warning light will be on or off. a. P is closed and Q is open. b. P is closed and Q is closed. c. P is open and Q is closed. d. P is open and Q is open.Warning Circuits The circuits shown in Excursion Exercises 15 and 16 include a switching network, a warning Light, and a battery. In each circuit the warning light will turn on only when the switching network is closed. An engineer thinks that the following circuit can be used in place of the circuit shown in Excursion Exercise 15. Do you agree? Explain.Determine whether each sentence is a statement. Star Wars: The Force Awakens is the greatest movie of all time.Determine whether each sentence is a statement. Harvey Mudd college is in Oregon.Determine whether each sentence is a statement. The area code for Storm Lake, Iowa, is 512.Determine whether each sentence is a statement. January 1. 2024. will be a Sunday.Determine whether each sentence is a statement. Have a fun trip.Determine whether each sentence is a statement. Do you like to read?Determine whether each sentence is a statement. Mickey Mouse was the first animated character to receive a star on the Hollywood Walk of Fame.Determine whether each sentence is a statement. Drew Brees is the starting quarterback of the Dallas Cowboys.Determine whether each sentence is a statement. x2=25Determine whether each sentence is a statement. x=x+1Determine the simple statements in each compound statement. The principal will attend the class on Tuesday or Wednesday.Determine the simple statements in each compound statement. 5 is an odd number and 6 is an even number.Determine the simple statements in each compound statement. A triangle is an acute triangle if and only if it has three acute angles.Determine the simple statements in each compound statement. If this is Saturday, then tomorrow is Sunday.Write the negation of each statement. The Giants lost the game.Write the negation of each statement. The lunch was served at noon.Write the negation of each statement. The game did not go into overtime.Write the negation of each statement. The game was not shown on ABC.Write each sentence in symbolic form. Represent each simple statement in the sentence with the letter indicated in the parentheses. Also state whether the sentence is a conjunction, a disjunction, a negation, a conditional, or a biconditional. If today is Wednesday (w), then tomorrow is Thursday (t).Write each sentence in symbolic form. Represent each simple statement in the sentence with the letter indicated in the parentheses. Also state whether the sentence is a conjunction, a disjunction, a negation, a conditional, or a biconditional. I went to the post office (p) and the bookstore (s).Write each sentence in symbolic form. Represent each simple statement in the sentence with the letter indicated in the parentheses. Also state whether the sentence is a conjunction, a disjunction, a negation, a conditional, or a biconditional. A triangle is an equilateral triangle (l) if and only if it is an equiangular triangle (a).22ESWite each sentence in symbolic form. Represent each simple statement in the sentence with the letter indicated in the parentheses. Also state whether the sentence is a conjunction, a disjunction, a negation, a conditional, or a biconditional. If it is a dog (d), it has fleas (f).Wite each sentence in symbolic form. Represent each simple statement in the sentence with the letter indicated in the parentheses. Also state whether the sentence is a conjunction, a disjunction, a negation, a conditional, or a biconditional. Polynomials that have exactly three terms (p) are called trinomials (t).Wite each sentence in symbolic form. Represent each simple statement in the sentence with the letter indicated in the parentheses. Also state whether the sentence is a conjunction, a disjunction, a negation, a conditional, or a biconditional. I will major in mathematics (in) or computer science (c).Wite each sentence in symbolic form. Represent each simple statement in the sentence with the letter indicated in the parentheses. Also state whether the sentence is a conjunction, a disjunction, a negation, a conditional, or a biconditional. All pentagons (p) have exactly five sides (s).Write each symbolic statement in words. Use p, q, r, s, r, and u as defined below. p: The tour goes to Italy. q: The tour goes to Spain. r: We go to Venice. s: We go to Florence. t: The hotel fees are included. u: The meals are not included. pqWrite each symbolic statement in words. Use p, q, r, s, r, and u as defined below. p: The tour goes to Italy. q: The tour goes to Spain. r: We go to Venice. s: We go to Florence. t: The hotel fees are included. u: The meals are not included. rsWrite each symbolic statement in words. Use p, q, r, s, r, and u as defined below. p: The tour goes to Italy. q: The tour goes to Spain. r: We go to Venice. s: We go to Florence. t: The hotel fees are included. u: The meals are not included. rsWrite each symbolic statement in words. Use p, q, r, s, r, and u as defined below. p: The tour goes to Italy. q: The tour goes to Spain. r: We go to Venice. s: We go to Florence. t: The hotel fees are included. u: The meals are not included. prWrite each symbolic statement in words. Use p, q, r, s, r, and u as defined below. p: The tour goes to Italy. q: The tour goes to Spain. r: We go to Venice. s: We go to Florence. t: The hotel fees are included. u: The meals are not included. srWrite each symbolic statement in words. Use p, q, r, s, r, and u as defined below. p: The tour goes to Italy. q: The tour goes to Spain. r: We go to Venice. s: We go to Florence. t: The hotel fees are included. u: The meals are not included. tuWrite each symbolic statement as an English sentence. Use p, q, r, s, and t as defined below. p: Taylor Swift is a singer. q: Taylor Swift is not a songwriter. r: Taylor Swift is an actress. s. Taylor Swift plays the piano. t: Taylor Swift does not play the guitar. (pr)qWrite each symbolic statement as an English sentence. Use p, q, r, s, and t as defined below. p: Taylor Swift is a singer. q: Taylor Swift is not a songwriter. r: Taylor Swift is an actress. s. Taylor Swift plays the piano. t: Taylor Swift does not play the guitar. s(pq)Write each symbolic statement as an English sentence. Use p, q, r, s, and t as defined below. p: Taylor Swift is a singer. q: Taylor Swift is not a songwriter. r: Taylor Swift is an actress. s. Taylor Swift plays the piano. t: Taylor Swift does not play the guitar. p(qr)Write each symbolic statement as an English sentence. Use p, q, r, s, and t as defined below. p: Taylor Swift is a singer. q: Taylor Swift is not a songwriter. r: Taylor Swift is an actress. s. Taylor Swift plays the piano. t: Taylor Swift does not play the guitar. (sq)tWrite each symbolic statement as an English sentence. Use p, q, r, s, and t as defined below. p: Taylor Swift is a singer. q: Taylor Swift is not a songwriter. r: Taylor Swift is an actress. s. Taylor Swift plays the piano. t: Taylor Swift does not play the guitar. (rq)qWrite each symbolic statement as an English sentence. Use p, q, r, s, and t as defined below. p: Taylor Swift is a singer. q: Taylor Swift is not a songwriter. r: Taylor Swift is an actress. s. Taylor Swift plays the piano. t: Taylor Swift does not play the guitar. t(rp)Write each sentence in symbolic form. Use p, q, r, and s as defined below. p: Stephen Curry is a football player. q: Stephen Curry is a basketball player. r: Stephen Curry is a rock star. s: Stephen Curry plays for the Warriors. Stephen Curry is a football player or a basketball player. and he is not a rock star.Write each sentence in symbolic form. Use p, q, r, and s as defined below. p: Stephen Curry is a football player. q: Stephen Curry is a basketball player. r: Stephen Curry is a rock star. s: Stephen Curry plays for the Warriors. Stephen Curry is a rock star, and he is not a basketball player or a football player.Write each sentence in symbolic form. Use p, q, r, and s as defined below. p: Stephen Curry is a football player. q: Stephen Curry is a basketball player. r: Stephen Curry is a rock star. s: Stephen Curry plays for the Warriors. If Stephen Curry is a basketball player and a rock star, then he is not a football player.Write each sentence in symbolic form. Use p, q, r, and s as defined below. p: Stephen Curry is a football player. q: Stephen Curry is a basketball player. r: Stephen Curry is a rock star. s: Stephen Curry plays for the Warriors. It is not true that. Stephen Curry is a football player or a rock star.Write each sentence in symbolic form. Use p, q, r, and s as defined below. p: Stephen Curry is a football player. q: Stephen Curry is a basketball player. r. Stephen Curry is a rock star. s: Stephen Curry plays for the Warriors. If Stephen Curry plays for the Warriors, then he is a basketball player and he is not a football player.Write each sentence in symbolic form. Use p, q, r, and s as defined below. p: Stephen Curry is a football player. q: Stephen Curry is a basketball player. r. Stephen Curry is a rock star. s: Stephen Curry plays for the Warriors. It is not true that. Stephen Curry is a football player or a rock star.Determine whether each statement is true or false. 75 or 31.Determine whether each statement is true or false. 39.Determine whether each statement is true or false. (1)50=1 and (1)90=1.Determine whether each statement is true or false. 73 or 9 is a prime number.Determine whether each statement is true or false. 511.Determine whether each statement is true or false. 4.55.4.Determine whether each statement is true or false. 2 is an odd number or 2 is an even number.Determine whether each statement is true or false. The square of any real number is a positive number.Write the negation of each quantified statement. Start each negation with Some, No, or All Some lions are playful.Write the negation of each quantified statement. Start each negation with Some, No, or All Some dogs are not friendly.Write the negation of each quantified statement. Start each negation with Some, No, or All All classic movies were first produced in black and white.Write the negation of each quantified statement. Start each negation with Some, No, or All Everybody enjoyed the dinner.Write the negation of each quantified statement. Start each negation with Some, No, or All No even numbers are odd numbers.Write the negation of each quantified statement. Start each negation with Some, No, or All Some actors are not rich.Write the negation of each quantified statement. Start each negation with Some, No, or All All cars run on gasoline.Write the negation of each quantified statement. Start each negation with Some, No, or All None of the students took my advice.Write Quotations in Symbolic Form In Exercises 61 to 64, translate each quotation into symbolic form. For each simple statement in the quotation, indicate what letter you used to represent the simple statement. If you can count your money, you dont have a billion dollars. J. Paul GettyWrite Quotations in Symbolic Form In Exercises 61 to 64, translate each quotation into symbolic form. For each simple statement in the quotation, indicate what letter you used to represent the simple statement. If you arent fired with enthusiasm, then you will he fired with enthusiasm. Vince Lombardi63ES64ES65ESWrite Statements in Symbolic Form In Exercises 65 to 70, translate each mathematical statement into symbolic form. For each simple statement in the given statement, indicate what letter you used to represent the simple statement. Any angle inscribed in a semicircle is a right angle.67ESWrite Statements in Symbolic Form In Exercises 65 to 70, translate each mathematical statement into symbolic form. For each simple statement in the given statement, indicate what letter you used to represent the simple statement. The sum of the measures of the three angles of any triangle is 180°.69ESWrite Statements in Symbolic Form In Exercises 65 to 70, translate each mathematical statement into symbolic form. For each simple statement in the given statement, indicate what letter you used to represent the simple statement. If the corresponding sides of two triangles are proportional, then the triangles are similar.Recreational Logic The following diagram shows two cylindrical teapots. The yellow teapot has the same diameter as the green teapot, but it is one and one-half times as tall as the green teapot. If the green teapot can hold a maximum of 6 cups of tea, then estimate the maximum number of cups of tea that the yellow teapot can hold. Explain your reasoning.Construct a closure (able for each of the following switching networks. Use the closure table to determine the required conditions for the network to be closed.Construct a closure (able for each of the following switching networks. Use the closure table to determine the required conditions for the network to be closed.Construct a closure (able for each of the following switching networks. Use the closure table to determine the required conditions for the network to be closed.Construct a closure (able for each of the following switching networks. Use the closure table to determine the required conditions for the network to be closed.Construct a closure (able for each of the following switching networks. Use the closure table to determine the required conditions for the network to be closed.Construct a closure (able for each of the following switching networks. Use the closure table to determine the required conditions for the network to be closed.Warning Circuits a. The following circuit shows a switching network used in an automobile. The warning buzzer will buzz only when the switching network is closed. Construct a closure table for the switching network. b. An engineer thinks that the following circuit can be used in place of the circuit in part a. Do you agree? Hint Construct a closure table for the switching network and compare your closure table with the closure table in part a.Determine the truth value of the compound statement given that p is a false statement, q is a true statement, and r is a true statement. P(qr)Determine the truth value of the compound statement given that p is a false statement, q is a true statement, and r is a true statement. r(pr)Determine the truth value of the compound statement given that p is a false statement, q is a true statement, and r is a true statement. (pq)(pq)Determine the truth value of the compound statement given that p is a false statement, q is a true statement, and r is a true statement. (pq)[ (pq)q ]5ES6ES7ESDetermine the truth value of the compound statement given that p is a false statement, q is a true statement, and r is a true statement. (pq)[ (pq)r ]9ES10ESa. Given that p is a false statement. what can be said about p(qr)? b. Explain why it is not necessary to know the truth values ofq and r to determine the truth value of p(qr) in part a above.12. a. Given that q is a true statement, what can be said about qr? b. Explain why it is not necessary to know the truth value of r to determine the truth value of qr in part a above.Construct a truth table for each compound statement. ~pqConstruct a truth table for each compound statement. (q~p)~qConstruct a truth table for each compound statement. p~q16ESConstruct a truth table for each compound statement. (p~q)[ ~(pq) ]18ES19ES20ES21ES22ES23ES24ES25ES26ES27ES28ES29ES30ES31ES32ESUse two truth tables to show that each of the statements are equivalent. p(qp),pq34ES35ESUse two truth tables to show that each of the statements are equivalent. [ (pq)r ][ (pq)r ][ p(qr) ],(pq)[ (pq)r ]Make use of one of De Morgans laws to write the given statement in an equivalent form. It is not true that, it rained or it snowed.Make use of one of De Morgans laws to write the given statement in an equivalent form. I did not pass the test and I did not complete the course.Make use of one of De Morgans laws to write the given statement in an equivalent form. She did not visit France and she did not visit Italy.Make use of one of De Morgans laws to write the given statement in an equivalent form. It is not true that. I bought a new car and I moved to Florida.Make use of one of De Morgans laws to write the given statement in an equivalent form. It is not true that, she received a promotion or that she received a raise.42ESUse a truth table to determine whether the given statement is a tautology. pq44ESUse a truth table to determine whether the given statement is a tautology. (pq)(pq)Use a truth table to determine whether the given statement is a tautology. (pq)(pq)47ES48ESUse a truth table to determine whether the given statement is a self-contradiction. rr50ES51ES52ESUse a truth table to determine whether the given statement is a self-contradiction. [ p(pq) ]q54ESExplain why the statement 78 is a disjunction.a. Why is the statement 57 true? b. Why is the statement 77 true?57ESExplain why no truth table can have exactly 100 rows.59ES60ESRecreational Logic A friend hands you the slip of paper shown below and challenges you to circle exactly four digits that have a sum of 19. Explain how you can meet this challenge.For each of the following, determine the output stream for the given input streams. a. b. c.2EEIdentify the antecedent and the consequent of each conditional statement. If had the money. I would buy the painting.Identify the antecedent and the consequent of each conditional statement. If Shelly goes on the trip, she will not be able to take part in the graduation ceremony.3ESIdentify the antecedent and the consequent of each conditional statement. If I dont get to school before 7:30, I wont be able to find a parking place.Identify the antecedent and the consequent of each conditional statement. If I change my major. I must reapply for admission.6ESDetermine the truth value of the given statement. If x is an even integer, then x2 is an even integer.Determine the truth value of the given statement. If x is a prime number, then x+2 is a prime number.Determine the truth value of the given statement. If all frogs can dance, then today is Monday.Determine the truth value of the given statement. If all cats are black, then I am a millionaire.Determine the truth value of the given statement. If 43, then 7=8.Determine the truth value of the given statement. If x2, then x+57.13ES14ES15ES16ES17ES18ES19ES20ES21ES22ES23ESConstruct a truth table for the given Statement. [ p(rq) ](rq)Write each conditional statement in its equivalent disjunctive form. If she could sing, she would be perfect for the part.26ESWrite each conditional statement in its equivalent disjunctive form. If x is an irrational number, then x is not a terminating decimal.28ESWrite each conditional statement in its equivalent disjunctive form. If the fog does not lift, our flight will be cancelled.Write each conditional statement in its equivalent disjunctive form. If she could sing, she would be perfect for the part. If he does not get frustrated, he will be able to complete the job. If x is an irrational number, then x is not a terminating decimal. If Mr. Hyde had a brain, he would be dangerous. If the fog does not lift, our flight will be cancelled. If the Yankees win the pennant. Carol will be happy.Write the negation of each conditional statement in its equivalent conjunctive form. If they offer me the contract, I will accept.32ESWrite the negation of each conditional statement in its equivalent conjunctive form. If pigs had wings, pigs could fly.Write the negation of each conditional statement in its equivalent conjunctive form. If we had a telescope, we could see that comet.Write the negation of each conditional statement in its equivalent conjunctive form. If she travels to Italy, she will visit her relatives.Write the negation of each conditional statement in its equivalent conjunctive form. If Paul could play better defense, he could be a professional basketball player.State whether the given biconditional is true or false. Assume that x and y are real number. x2=9 if and only if x=3.38ES39ESState whether the given biconditional is true or false. Assume that x and y are real number | x+y |=x+y if and only if x+y0.State whether the given biconditional is true or false. Assume that x and y are real number. A number is a rational number if and only if the number can be written as a terminating decimal.State whether the given biconditional is true or false. Assume that x and y are real number 0.3 is a rational number if and only if 13 is a rational number.State whether the given biconditional is true or false. Assume that x and y are real number 4=7 if and only if 2=3.State whether the given biconditional is true or false. Assume that x and y are real number 44. x is an even number if and only if x is not an odd numberState whether the given biconditional is true or false. Assume that x and y are real number Triangle ABC is an equilateral triangle if and only if triangle ABC is an equiangular triangle.State whether the given biconditional is true or false. Assume that x and y are real number. Today is March 1 if and only if yesterday was February 28.Write each sentence in symbolic form. Use v, p, and t as defined below. v: 1 will take a vacation. p: I get the promotion. t: I will be transferred. I will take a vacation if and only if I get the promotion.Write each sentence in symbolic form. Use v, p, and t as defined below. v: 1 will take a vacation. p: I get the promotion. t: I will be transferred. If I do not get the promotion, then I will be transferred and I will not take a vacation.Write each sentence in symbolic form. Use v, p, and t as defined below. v: 1 will take a vacation. p: I get the promotion. t: I will be transferred. If I get the promotion. I will take a vacation.Write each sentence in symbolic form. Use v, p, and t as defined below. v: 1 will take a vacation. p: I get the promotion. t: I will be transferred. If I am not transferred. I will take a vacation.Write each sentence in symbolic form. Use v, p, and t as defined below. v: 1 will take a vacation. p: I get the promotion. t: I will be transferred. If I am transferred, then I will not take a vacation.52ESWrite each sentence in symbolic form. Use v, p, and t as defined below. v: 1 will take a vacation. p: I get the promotion. t: I will be transferred. If I am not transferred and I get the promotion, then I will take a vacation.54ES55ES56ES57ES58ES59ES60ESThe statement, All squares are rectangles. can be written as If a figure is a square, then it is a rectangle. Write each statement given in All Xs are Ys form in the form If ills an X. then it is a Y All rational numbers are real numbers.62ES63ESThe statement, All squares are rectangles. can be written as If a figure is a square, then it is a rectangle. Write each statement given in All Xs are Ys form in the form If ills an X. then it is a Y All paintings by Vincent van Gogh are valuable.Recreational Logic The field of a new soccer stadium is watered by three individual sprinkler systems, as shown by the A. B. and C regions in the figure at the right. Each sprinkler system is controlled by exactly one of three on-off valves in an underground maintenance room, and each sprinkler system can be turned on without turning on the other two systems. Each of the valves is presently in the off position, and the field is dry. The valves have not been labeled, so you do not know which valve controls which sprinkler system. You want to correctly label the valves as A. B. and C. You also want to do it by making only one trip up to the field. You cannot see the field from the maintenance room, and no one is available to help you. What procedure can you use to determine how to correctly label the valves? Assume that all of the valves and all of the sprinkler systems are operating properly. Also assume that the sprinklers are either completely off or completely on. Explain your reasoning.66ES1. a. Complete a truth table for p(qq). b. Use the results of Excursion Exercise 1a to determine an equivalent statement for p(qq).2EE3. a. Determine the output stream for the following network of NAND gates. Note:In a network of logic gates. a solid circle is used to indicate a connection. A symbol such as is used to indicate no connection. b. What logic gate is modeled by the network in Figure 3.14?NAND gates are functionally complete in that any logic gate can be constructed using only NAND gates. Construct a network of NAND gates that would produce the same output stream as an OR gate.Write each statement in if p, then q form. We will be in good shape for the ski trip provided that we take the aerobics class.2ESWrite each statement in if p, then q form. Every odd prime number is greater than 2.4ESWrite each statement in if p, then q form. Every theropod is carnivorous.6ESWrite each statement in if p, then q form. I will be able to prepare for the test only if I have the text book.8ES9ES10ESWrite the a. converse, b. inverse, and c. contrapositive of the given statement. If I were rich. I would quit this job.Write the a. converse, b. inverse, and c. contrapositive of the given statement. If we had a car, then we would be able to take the class.13ESWrite the a. converse, b. inverse, and c. contrapositive of the given statement. I will be in the talent show only if I can do the same comedy routine I did for the banquet.Write the a. converse, b. inverse, and c. contrapositive of the given statement. Every parallelogram is a quadrilateral.Write the a. converse, b. inverse, and c. contrapositive of the given statement. If you get the promotion, you will need to move to Denver.Write the a. converse, b. inverse, and c. contrapositive of the given statement. I would be able to get current information about astronomy provided I had access to the Internet.18ESWrite the a. converse, b. inverse, and c. contrapositive of the given statement. You need four-wheel drive to make the trip to Death Valley.Write the a. converse, b. inverse, and c. contrapositive of the given statement. If you are the president of the United States, then your age is at least 35.Write the a. converse, b. inverse, and c. contrapositive of the given statement. She will visit Kauai only if she can extend her vacation for at least two days.Write the a. converse, b. inverse, and c. contrapositive of the given statement. In a right triangle, the acute angles are complementary.Write the a. converse, b. inverse, and c. contrapositive of the given statement. Two lines perpendicular to a given line are parallel.Write the a. converse, b. inverse, and c. contrapositive of the given statement. If x+5=12, then x=7.Determine whether the given statements are equivalent. If Kevin wins, we will celebrate. If we celebrate, then Kevin will win.Determine whether the given statements are equivalent. If I save $1000. I will go on the field trip. If I go on the field trip, then I saved $1000.27ESDetermine whether the given statements are equivalent. If you understand algebra. you can remember algebra. If you do not understand algebra. you cannot remember algebra.Determine whether the given statements are equivalent. If ab ,then acbc. If ab. then acbc.30ES31ES32ES33ES34ESWrite the contrapositive of the statement and use the contrapositive to determine whether the given statement is true or false. If a+b5, then a+b25.Write the contrapositive of the statement and use the contrapositive to determine whether the given statement is true or false. If x2 is an even integer, then x is an even integer. (Assume x is an integer.)37ES38ES39ESGive an example of a true conditional statement whose a. inverse is true. b. inverse is false.Determine the original statement if the given statement is related to the original in the manner indicated. 41. Converse: If you can do it, you can dream it.Determine the original statement if the given statement is related to the original in the manner indicated. 42. Inverse: If I did not have a dime. I would not spend it.Determine the original statement if the given statement is related to the original in the manner indicated. 43. Contrapositive: If I were a singer, I would not be a dancer.44ES45ES46ESA Puzzle Lewis Carroll (Charles Dodgson) wrote many puzzles. many of which he recorded in his diaries. Solve the following puzzle. which appears in one of his diaries. The Dodo says that the Hatter tells lies. The Hatter says that the March Hare tells lies. The March Hare says that both the Dodo and the Hatter tell lies. Who is telling the truth? Hint: Consider the three different cases in which only one of the characters is telling the truth. In only one of these cases can all three of the statements be true.