In Exercises 43–48, write the converse, inverse, and contrapositive of the statement in sentence form. If the water is running, then Linus is getting a drink.
> In Exercises 13–32, determine whether the argument is valid or invalid. You may compare the argument to a standard form, given on page 140, or use a truth table.
> In Exercises 13–32, determine whether the argument is valid or invalid. You may compare the argument to a standard form, given on page 140, or use a truth table.
> In Exercises 13–32, determine whether the argument is valid or invalid. You may compare the argument to a standard form, given on page 140, or use a truth table.
> In Exercises 13–32, determine whether the argument is valid or invalid. You may compare the argument to a standard form, given on page 140, or use a truth table.
> In Exercises 9–16, use a truth table to determine whether the two statements are equivalent. q ( p, (p ( (q
> Convert each of the following to a numeral in the base indicated. 39,885 to base 16
> In Exercises 9–16, use a truth table to determine whether the two statements are equivalent. (q ( (p, p ( q
> In Exercises 9–16, use a truth table to determine whether the two statements are equivalent. (( p ( q), p ( (q
> In Exercises 9–16, use a truth table to determine whether the two statements are equivalent. p ( q, (p ( q
> Kakuro Refer to the Recreational Mathematics box on page 130. Complete the following Kakuro puzzle.
> In Exercises 27–31, insert the symbol , or = in the shaded area to make a true statement.
> In symbolic logic, a statement is either true or false (consider true to have a value of 1 and false a value of 0). In fuzzy logic, nothing is true or false, but everything is a matter of degree. For example, consider the statement “The
> Determine whether ( [(( p ( (q)]( p ( (q. Explain the method(s) you used to determine your answer.
> We learned that p ( q ( (p ( q. Determine a conjunction that is equivalent to p ( q. (Hint: There are many answers.)
> If p and q represent two simple statements, and if p ( q is a true statement, what must be the truth value of the contrapositive, (q ( (p? Explain.
> If p and q represent two simple statements, and if p S q isa false statement, what must be the truth value of the contrapositive, ,q S ,p? Explain.
> If p and q represent two simple statements, and if p ( q is a false statement, what must be the truth value of the inverse, (p ( (q? Explain.
> Purchasing DVDs The manager of the video department at Target plans to purchase a large number of DVDs of The Lego Movie. One supplier is selling boxes of 20 DVD movies for $240, and a second supplier is selling boxes of 12 DVD movies for $180. Only comp
> If p and q represent two simple statements, and if p ( q is a false statement, what must be the truth value of the converse, q ( p? Explain.
> In Exercises 55–68, determine which, if any, of the three statements are equivalent (see Example 13). (a) The mortgage rate went down, if and only if Tim purchased the house and the down payment was 10%. (b) The down payment was 10%, and if Tim purchas
> In Exercises 55–68, determine which, if any, of the three statements are equivalent (see Example 13). (a) The package was sent by Federal Express, or the package was not sent by United Parcel Service but the package arrived on time. (
> In Exercises 27–31, insert the symbol , or = in the shaded area to make a true statement.
> In Exercises 55–68, determine which, if any, of the three statements are equivalent (see Example 13). (a) If you are 18 years old and a citizen of the United States, then you can vote in the presidential election. (b) You can vote in the presidential e
> In Exercises 55–68, determine which, if any, of the three statements are equivalent (see Example 13). (a) If the pay is good and today is Monday, then I will take the job. (b) If I do not take the job, then it is false that the pay is good or today is
> In Exercises 55–68, determine which, if any, of the three statements are equivalent (see Example 13). (a) Fitz and the Tantrums will not go on tour if and only if James King does not play the saxophone (b) It is false that Fitz and the Tantrums
> In Exercises 55–68, determine which, if any, of the three statements are equivalent (see Example 13). (a) If the corn bag goes in the hole, then you are awarded three points. (b) It is false that the corn bag goes in the hole and you
> In Exercises 55–68, determine which, if any, of the three statements are equivalent (see Example 13). (a) Mr. Patrick is chosen as department chair if and only if he is the only candidate. (b) If Mr. Patrick is chosen as department chair then he is the
> In Exercises 55–68, determine which, if any, of the three statements are equivalent (see Example 13). (a) The grass grows and the trees are blooming. (b) If the trees are blooming, then the grass does not grow. (c) The trees are not blooming or the gr
> In Exercises 55–68, determine which, if any, of the three statements are equivalent (see Example 13). (a) If Tim is the director then Johnny is the actor. (b) Tim is not the director or Johnny is the actor. (c) It is false that Tim is the director and
> Convert each of the following to a numeral in the base indicated. 9455 to base 16
> Grass Seed A bag of Turf Builder Sun and Shade Mix grass seed covers an area of 4000 ft2. How many bags are needed to cover an area of 35,000 ft2?
> In Exercises 55–68, determine which, if any, of the three statements are equivalent (see Example 13). (a) We do not go hiking or we go fishing. (b) If we go hiking, then we do not go fishing. (c) If we go fishing, then we do not go h
> In Exercises 27–31, insert the symbol , or = in the shaded area to make a true statement.
> In Exercises 55–68, determine which, if any, of the three statements are equivalent (see Example 13). (a) Cher did not sing “Believe” or Sting did not sing “Russians.” (b) If Cher sang “Believe” then Sting sang “Russians.” (c) It is false that Sting
> In Exercises 55–68, determine which, if any, of the three statements are equivalent (see Example 13). (a) The shoes are not on sale but the purse is on sale. (b) If the shoes are not on sale then the purse is not on sale. (c) It is false that the shoe
> In Exercises 55–68, determine which, if any, of the three statements are equivalent (see Example 13). (a) If Fido is our dog’s name, then Rex is not our dog’s name. (b) It is false that Fido is our dog’s name and Rex is not our dog’s name. (c) Fido is
> In Exercises 55–68, determine which, if any, of the three statements are equivalent (see Example 13). (a) If the player gets a red card, then the player sits out. (b) If the player sits out, then the player gets a red card. (c) The player does not sit
> In Exercises 49–54, write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement is true or false.
> In Exercises 49–54, write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement is true or false. If two lines do not intersect in at least one point, then the two lines are parallel.
> In Exercises 49–54, write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement is true or false. If 1/n is not a natural number, then n is not a natural number.
> In Exercises 49–54, write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement is true or false. If a natural number is divisible by 3, then the natural number is divisible by 6.
> In Exercises 49–54, write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement is true or false. If the quadrilateral is a parallelogram, then the opposite sides are parallel.
> Making Rice Following are the amounts of ingredients recommended to make various servings of Uncle Ben’s Original Converted Rice. Note: 1 tbsp = 3 tsp. Determine the amount of each ingredient needed to make 8 servings using the followin
> In Exercises 27–31, insert the symbol , or = in the shaded area to make a true statement.
> In Exercises 49–54, write the contrapositive of the statement. Use the contrapositive to determine whether the conditional statement is true or false. If a natural number is divisible by 14, then the natural number is divisible by 7.
> In Exercises 43–48, write the converse, inverse, and contrapositive of the statement in sentence form. If Grandma is not available to babysit, then we cannot go to the movie.
> In Exercises 43–48, write the converse, inverse, and contrapositive of the statement in sentence form. If the menu includes calzones, then I do not stay on my diet.
> In Exercises 43–48, write the converse, inverse, and contrapositive of the statement in sentence form. If the sun is shining, then we take out the sailboat.
> In Exercises 43–48, write the converse, inverse, and contrapositive of the statement in sentence form. If I go to Mexico, then I buy silver jewelry.
> In Exercises 43–48, write the converse, inverse, and contrapositive of the statement in sentence form. If Nanette teaches macramé, then she needs extra yarn.
> In Exercises 37– 42, use the fact that ((p ( q) is equivalent to p ( (q to write the statement in an equivalent form. Thompson is sick today but Allen didn’t go to school.
> In Exercises 37– 42, use the fact that ((p ( q) is equivalent to p ( (q to write the statement in an equivalent form. It is not true that if Amazon has a sale then we will buy $100 worth of books.
> In Exercises 37– 42, use the fact that ((p ( q) is equivalent to p ( (q to write the statement in an equivalent form. The Badgers beat the Nittany Lions and the Bucks beat the 76ers
> In Exercises 27–31, insert the symbol , or = in the shaded area to make a true statement.
> Convert each of the following to a numeral in the base indicated. 13,312 to base 12
> In Exercises 37– 42, use the fact that ((p ( q) is equivalent to p ( (q to write the statement in an equivalent form. I am cold and the heater is not working.
> In Exercises 37– 42, use the fact that ((p ( q) is equivalent to p ( (q to write the statement in an equivalent form. It is false that if General Electric makes the telephone, then the telephone is made in the United States.
> In Exercises 37– 42, use the fact that ((p ( q) is equivalent to p ( (q to write the statement in an equivalent form. It is false that if we go to Chicago, then we will go to Navy Pier
> In Exercises 31–36, use the fact that p ( q is equivalent to (p ( q to write an equivalent form of the given statement. If Weezer is not on the radio, then Oly is working
> In Exercises 31–36, use the fact that p ( q is equivalent to (p ( q to write an equivalent form of the given statement. The Foo Fighters will practice or they will not sound good.
> In Exercises 31–36, use the fact that p ( q is equivalent to (p ( q to write an equivalent form of the given statement. If Joanne goes to the Lightning game, then she will not go to the Rays game.
> In Exercises 31–36, use the fact that p ( q is equivalent to (p ( q to write an equivalent form of the given statement. Chase is not hiding or the pitcher is broken.
> In Exercises 31–36, use the fact that p ( q is equivalent to (p ( q to write an equivalent form of the given statement. Byron did not walk to the meeting or we started late.
> In Exercises 31–36, use the fact that p ( q is equivalent to (p ( q to write an equivalent form of the given statement. If Janette buys a new car, then she sells her old car.
> 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. /
> In Exercises 25–30, use De Morgan’s laws to write an equivalent statement for the given sentence If Phil buys us dinner, then we will not go to the top of the CN Tower but we will be able to walk to the Red Bistro Restaurant.
> Making Cream of Wheat The following amounts of ingredients are recommended to make various servings of Nabisco Instant Cream of Wheat. Note: 16 tbsp = 1 cup. Determine the amount of each ingredient needed to make 3 servings using the following procedures
> In Exercises 25–30, use De Morgan’s laws to write an equivalent statement for the given sentence If Ashley takes the new job, then she will not move or she will buy a new house in town.
> In Exercises 25–30, use De Morgan’s laws to write an equivalent statement for the given sentence The pot roast is hot, but it is not well done.
> In Exercises 25–30, use De Morgan’s laws to write an equivalent statement for the given sentence The dog was not a bulldog and the dog was not a boxer.
> In Exercises 25–30, use De Morgan’s laws to write an equivalent statement for the given sentence It is false that the Camaro is a Dodge or the Challenger is a Chevy.
> In Exercises 25–30, use De Morgan’s laws to write an equivalent statement for the given sentence It is false that Taylor Swift is a country singer and Wiz Khalifa sings opera.
> In Exercises 17–24, use De Morgan’s laws to determine whether the two statements are equivalent. q( (( p ( (r ), q ( (p ( r
> In Exercises 17–24, use De Morgan’s laws to determine whether the two statements are equivalent. (( p ( (q)(r,(( p ( q)( r
> In Exercises 17–24, use De Morgan’s laws to determine whether the two statements are equivalent. ((( p ( q), p ( (q
> Convert each of the following to a numeral in the base indicated. 23 to base 3
> proper subset oIn Exercises 3–12, show that the set is infinite by placing it in a one-to-one correspondence with a f itself. Be sure to show the pairing of the general terms in the sets.
> In Exercises 17–24, use De Morgan’s laws to determine whether the two statements are equivalent. ((( p ( q), p ( (q
> In Exercises 17–24, use De Morgan’s laws to determine whether the two statements are equivalent. (( p ( q), (p ( (q
> Convert each of the following to a numeral in the base indicated. 9004 to base 12
> In Exercises 17–24, use De Morgan’s laws to determine whether the two statements are equivalent. (( p ( q), (p ( (q
> In Exercises 17–24, use De Morgan’s laws to determine whether the two statements are equivalent. (( p ( q), (p ( (q
> In Exercises 17–24, use De Morgan’s laws to determine whether the two statements are equivalent. (( p ( q), (p ( (q
> In Exercises 9–16, use a truth table to determine whether the two statements are equivalent. (p ( q) ( r, p ( (q ( r)
> In Exercises 9–16, use a truth table to determine whether the two statements are equivalent. ( p ( q) ( (q ( p), ( p ( q)
> In Exercises 9–16, use a truth table to determine whether the two statements are equivalent. p ( (q ( r), ( p ( q) ( r
> In Exercises 9–16, use a truth table to determine whether the two statements are equivalent. (p ( q) ( r, p ( (q ( r)
> Height of a Tree At a given time of day, the ratio of the height of an object to the length of its shadow is the same for all objects. If a 3-ft stick in the ground casts a shadow of 1.2 ft, find the height of a tree that casts a shadow that is 15.36 ft.
> In Exercises 7–16, construct a truth table for the statement. ((p (q)
> The Youngest Triplet The Barr triplets have an annoying habit: Whenever a question is asked of the three of them, two tell the truth and the third lies. When I asked them which of them was born last, they replied as follows. Mary: Katie was born last. Ka
> At Puzzle Solve the following puzzle. The Joneses have four cats. The parents are Tiger and Boots, and the kittens are Sam and Sue. Each cat insists on eating out of its own bowl. To complicate matters, each cat will eat only its own brand of cat food. T
> Buying a Boat Four partners decide to share the cost of a boat equally. By bringing in an additional partner, they can reduce the cost to each of the five partners by $3000. What is the total cost of the boat?
> Satisfiability Problem Refer to the Recreational Mathematics box on page 119 and then solve the following satisfiability problem. Allen, Booker, Chris, and Dennis all were born in the same year—one in January, one in February, one in March, and one in Ap
> Construct a truth table for (a) ( p ( q )((r ( s ) (b) ( q ( (p ) ( (r ( s )
> In Exercises 71 and 72, construct truth tables for the symbolic statement. [ ( r ( (q )((] ( ( q((r)
> In Exercises 71 and 72, construct truth tables for the symbolic statement. [p ( (q ( ( r)] ((p ( ( q)
> Suppose both of the following statements are false. p: Muhundan spoke at the teachers’ conference. q: Muhundan received the outstanding teacher award. Find the truth values of each compound statement. Job Interview Consider the statement “If your interv
> Suppose both of the following statements are false. p: Muhundan spoke at the teachers’ conference. q: Muhundan received the outstanding teacher award. Find the truth values of each compound statement. A New Computer Your parents make the following stat
> 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. {3, 9, 27, 81, 243, …}
> Suppose both of the following statements are false. p: Muhundan spoke at the teachers’ conference. q: Muhundan received the outstanding teacher award. Find the truth values of each compound statement. If Muhundan did not receive the outstanding teacher
