A Concise Introduction to Logic 13th edition Patrick J. Hurley, Lori Watson - Solutions

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(a) Show that p ( [q( ( p ˄ q)] (b) True or false? p([q ( (p ˄ q)]
1. True or false? (p ˅ q) ( [q ( (p ˄ q)] 2. True or false? [p ˅ ( p ˄ q)] ( p
Write a statement equivalent to ( (p ˅ q) ˄ (q, Using only ( and (?
Show that the argument is valid. 1. The auto manufacturer follows environmental regulations or they face legal action. The manufacturer does not follow environmental regulations. Therefore, the manufacturer faces legal action. 2. If the class votes for an oral final, the teacher is glad. If the
Test the validity of the arguments.1. If the salaries go up, then more people apply. More people apply or the salaries go up. Therefore, the salaries go up.2. If Rita studies, she gets good grades. Rita gets bad grades. Therefore, Rita does not study.3. The balloon is yellow or the ribbon is pink.
Use indirect proof to show that the argument is valid. 1. Sam goes to the store only if he needs milk. Sam does not need milk. Therefore, Sam does not go to the store. 2. If it rains hard, there will be no picnic. If Dave brings the Frisbee, the kids will be happy. The kids are not happy and there
Show that each of the arguments in Exercises 1 and 2 is valid, first by using a direct proof and then by using an indirect proof.1. If Jimmy does not find the keys, he will do his homework. Jimmy does not do his homework. Show that Jimmy found his keys.2. If spring vacation includes Easter, Simone
Show that each of the arguments in Exercises 1 and 2 is valid by using a direct proof or by using an indirect proof.1. If Marissa does not go to the movies, then she is not idle. If Marissa is not in a knitting class, she is idle. Marissa is not in a knitting class. Therefore, Marissa goes to the
Let U = {1, 2, 3, 4, 5, 6}. Determine the truth value of p(x) = [(x is even) or (x is divisible by 3)] for the given values of x. (a) x = 1 (b) x = 4 (c) x = 3 (d) x = 6 (e) x = 5
Let the universe consist of all real numbers. Let p(x) = (x is positive) and q(x) = (x is a perfect square). Determine the truth value of each of the following: (a) (x p(x) (b) (x q(x) (c) ∃x p(x) (d) ∃x q(x) (e) ∃x [p(x) ( q(x)] (f) ∃x [q(x) ( p(x)] (g) (x [p(x) ( q(x)] (h) (x [q(x) (
Negate each statement by changing existential quantifiers to universal quantifiers, or vice versa. (a) Every dog has its day. (b) Some men fight wars. (c) All women are married. (d) For every pot, there is a cover. (e) Not all children have pets. (f) Not every month has 30 days?
Negate each statement by changing existential quantifiers to universal quantifiers, or vice versa. (a) Every stitch saves time. (b) All books have hard covers. (c) Some children are afraid of snakes. (d) Not all computers have a hard disk. (e) Some chairs do not have arms?
Consider the universe of nonnegative integers = {0, 1, 2, 3, 4, . . . .}. Write the English sentence for each symbolic statement. Determine the truth value of each statement. If the statement is false, give a counterexample and write its negation out in words. (a) (x (y [x + y > 12] (b) (x ∃y [x
Consider the universe of all subsets of the set A = {a, b, c}. Let the variables x and y denote subsets of A. Find the truth value of each of the statements, and explain your answer. If the statement is false, give a counterexample. (a) (x (y [x ⊆ y] (b) (x (y [(x ⊆ y) ˅ (y ⊆ x)] (c) ∃x (y
Let the universe for both variables x and y be the set {1, 2, 3, 4, 5, 6}. Let p(x, y) = "x divides y." Give the truth values of each of the statements; explain your answer, and give a counterexample in the case that the statement is false. (a) (x (y p(x, ( y) (b) (x ∃y p(x, y) (c) ∃x (y p(x,
1. If p(x) denotes "x ∈ S" and q(x) denotes "x ∈ T," describe the following, using logical statement forms with p(x) and q(x): (a) x ∈ S' ( T' (b) x ∈ S ( T ′ (c) x ∈ S′ ( T ′ (d) x ∈ (S ( T )′ 2. Let the universal set be U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, let
1. Is S a subset of T? Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} S = {x ∈ U: x divides 12 evenly} T = {x ∈ U: x is a multiple of 2}. 2. Prove that S is a subset of T, where U = {1, 2, 3, 4, 5, 6, 7, 8, 9} S = {x ∈ U: x is a multiple of 2} T = {x ∈ U: x divides 24 evenly}. 3. Prove
Determine the truth value of p(x) for the values of x chosen from the universe of all letters of the alphabet, where p(x) = [(x is a vowel) and (x is in the word ABLE)]. (a) x = A (b) x = D (c) x = B (d) x = I
1. An alert California teacher chided "Dear Abby" (Baltimore Sun, March 1, 1989) for her statement "Confidential to Eunice: All men do not cheat on their wives." Let p(x) be the statement "x cheats on his wife" in the universe of all men. Write Abby's statement symbolically. Rewrite the statement,
Let the universe be all university professors. Let p(x) be the open statement "x likes poetry." Write the following statements symbolically: (a) All university professors like poetry. (b) Some university professors do not like poetry. (c) Some university professors like poetry. (d) Not all
Consider the universe of all orange juice. Write the following symbolically, using p(x) = "x comes from Florida." (a) All orange juice does not come from Florida. (b) Some orange juice comes from Florida. (c) Not all orange juice comes from Florida. (d) Some orange juice does not come from
1. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let p(x) = [(x is prime) ( (x2 + 1 is even)]. Find the truth value of (a) ∃x p(x) (b) (x p(x) 2. Let U = {0, 1, 2, 3, 4}. Let p(x) = [x2 > 9]. Find the truth value of (a) ∃x p(x) (b) (x p(x)
Let the universe consist of all nonnegative integers. Let p(x) be the statement "x is even." Let q(x) be the statement "x is odd." Determine the truth value of (a) (x [p(x) ˅ q(x)] (b) [(x p(x)] ˅ [(x q(x)] (c) ∃x [p(x) ˅ q(x)] (d) ∃x [p(x) ˄ q(x)] (e) (x [p(x) ( q(x)] (f) [∃x p(x)] ˄
1. Write the logic statement represented by Fig. 10.2. Write the logic statement represented by Fig. 11. 3. Write the logic statement represented by Fig. 12. 4. Write the logic statement represented by Fig. 13.
Simplify the logic circuit in Fig. 15 as much as possible.Figure 15:
Simplify the logic circuit in Fig. 16 as much as possible.Figure 16:
1. Simplify the logic circuit in Fig. 17 as much as possible.Figure 17:2. Design a logic circuit with two inputs (use p and q) that always has output 1?
1. Design a logic circuit with two inputs (use p and q) that always has output 0. 2. Design a logic circuit that acts as an or gate for inputs p and q, using three nor gates?
1. Design a logic circuit that acts as an and gate for inputs p and q, using three NAND gates. 2. Design a logic circuit that acts as an XOR gate for inputs p and q, using three gates other than XOR or or?
Design a logic circuit for (p NAND q) NAND (p NAND q), and show the outputs for all values of p and q on a truth table?
1. In the game of "match," each of two players, A and B, has control of an input switch. At the signal, each player allows the current to flow (on) or stops the current (off). If both players choose the same input (both on or both off), player A wins. If their inputs differ, player B wins. Design a
Draw the logic circuit that represents each of the logical statements in Exercises 5-8. Determine the output when the variables have the values given? 1. p ˄ ((q ˅ r); for p = 1, q = 0, r = 1 2. (p ˄ q) ˅ (p ˅ r); for p = 1, q = 0, r = 1 3. ((p ˅ (q) ˄ ((p ˄ r); for p = 1, q = 0, r = 1 4. (
Simplify the logic circuit in Fig. 14 as much as possible.Figure 14:
Carbon monoxide molecules happen to be just the right size and shape, and happen to have just the right chemical properties, to fit neatly into cavities within hemoglobin molecules in blood that are normally reserved for oxygen molecules. Consequently, carbon monoxide diminishes the oxygen-carrying
Punishment, when speedy and specific, may suppress undesirable behavior, but it cannot teach or encourage desirable alternatives. Therefore, it is crucial to use positive techniques to model and reinforce appropriate behavior that the person can use in place of the unacceptable response that has to
Profit serves a very crucial function in a free-enterprise economy, such as our own. High profits are the signal that consumers want more of the output of the industry. High profits provide the incentive for firms to expand output and for more firms to enter the industry in the long run. For a firm
Cats can think circles around dogs! My cat regularly used to close and lock the door to my neighbor's doghouse, trapping their sleeping Doberman inside. Try telling a cat what to do, or putting a leash on him-he'll glare at you and say, "I don't think so. You should have gotten a dog." Each of the
Since private property helps people define themselves, since it frees people from mundane cares of daily subsistence, and since it is finite, no individual should accumulate so much property that others are prevented from accumulating the necessities of life. Each of the following passages contains
To every existing thing God wills some good. Hence, since to love any thing is nothing else than to will good to that thing, it is manifest that God loves everything that exists. Each of the following passages contains a single argument. Using the letters "P" and "C," identify the premises and
Women of the working class, especially wage workers, should not have more than two children at most. The average working man can support no more and the average working woman can take care of no more in decent fashion. Each of the following passages contains a single argument. Using the letters "P"
Radioactive fallout isn't the only concern in the aftermath of nuclear explosions. The nations of planet Earth have acquired nuclear weapons with an explosive power equal to more than a million Hiroshima bombs. Studies suggest that explosion of only half these weapons would produce enough soot,
An ant releases a chemical when it dies, and its fellows then carry it away to the compost heap. Apparently the communication is highly effective; a healthy ant painted with the death chemical will be dragged to the funeral heap again and again. Each of the following passages contains a single
Every art and every inquiry, and similarly every action and pursuit, is thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim. Each of the following passages contains a single argument. Using the letters "P" and "C," identify the
Poverty offers numerous benefits to the nonpoor. Antipoverty programs provide jobs for middle-class professionals in social work, penology, and public health. Such workers' future advancement is tied to the continued growth of bureaucracies dependent on the existence of poverty. Each of the
Since the good, according to Plato, is that which furthers a person's real interests, it follows that in any given case when the good is known, men will seek it. Each of the following passages contains a single argument. Using the letters "P" and "C," identify the premises and conclusion of each
Corn is an annual crop. Butcher's meat, a crop which requires four or five years to grow. As an acre of land, therefore, will produce a much smaller quantity of the one species of food than the other, the inferiority of the quantity must be compensated by the superiority of the price. Each of the
Neither a borrower nor lender be For loan oft loses both itself and friend, And borrowing dulls the edge of husbandry. Each of the following passages contains a single argument. Using the letters "P" and "C," identify the premises and conclusion of each argument, writing premises first and
The stakes in whistle-blowing are high. Take the nurse who alleges that physicians enrich themselves in her hospital through unnecessary surgery; the engineer who discloses safety defects in the braking systems of a fleet of new rapid-transit vehicles; the Defense Department official who alerts
If a piece of information is not "job relevant," then the employer is not entitled qua employer to know it. Consequently, since sexual practices, political beliefs, associational activities, etc., are not part of the description of most jobs, that is, since they do not directly affect one's job
Many people believe that a dark tan is attractive and a sign of good health, but mounting evidence indicates that too much sun can lead to health problems. One of the most noticeable effects is premature aging of the skin. The sun also contributes to certain types of cataracts, and, what is most
Contrary to the tales of some scuba divers, the toothy, gaping grin on the mouth of an approaching shark is not necessarily anticipatory. It is generally accepted that by constantly swimming with its mouth open, the shark is simply avoiding suffocation. This assures a continuous flow of
Not only is the sky blue [as a result of scattering], but light coming from it is also partially polarized. You can readily observe this by placing a piece of Polaroid (for example, one lens of a pair of Polaroid sunglasses) in front of your eye and rotating it as you look at the sky on a clear
Since the secondary light [from the moon] does not inherently belong to the moon and is not received from any star or from the sun, and since in the whole universe there is no other body left but the earth, what must we conclude? What is to be proposed? Surely we must assert that the lunar body (or
Anyone familiar with our prison system knows that there are some inmates who behave little better than brute beasts. But the very fact that these prisoners exist is a telling argument against the efficacy of capital punishment as a deterrent. If the death penalty had been truly effective as a
Though it is possible that REM sleep and dreaming are not necessary in the adult, REM deprivation studies seem to suggest otherwise. Why would REM pressure increase with deprivation if the system is unimportant in the adult? Each of the following passages contains a single argument. Using the
As the denial or perversion of justice by the sentences of courts, as well as in any other manner, is with reason classed among the just causes of war, it will follow that the federal judiciary ought to have cognizance of all causes in which the citizens of other countries are concerned. Each of
We say that an end pursued in its own right is more complete than an end pursued because of something else, and that an end that is never choiceworthy because of something else is more complete than ends that are choiceworthy both in their own right and because of this end. Hence, an end that is
When individuals voluntarily abandon property, they forfeit any expectation of privacy in it that they might have had. Therefore, a warrantless search or seizure of abandoned property is not unreasonable under the Fourth Amendment. Each of the following passages contains a single argument. Using
Artists and poets look at the world and seek relationships and order. But they translate their ideas to canvas, or to marble, or into poetic images. Scientists try to find relationships between different objects and events. To express the order they find, they create hypotheses and theories. Thus
The fact that there was never a land bridge between Australia and mainland Asia is evidenced by the fact that the animal species in the two areas are very different. Asian placental mammals and Australian marsupial mammals have not been in contact in the last several million years. Each of the
It really does matter if you get enough sleep. We need sleep to think clearly, react quickly, and create memories. Studies show that people who are taught mentally challenging tasks do better after a good night's sleep. Other research suggests that sleep is needed for creative problem solving. Each
The classroom teacher is crucial to the development and academic success of the average student, and administrators simply are ancillary to this effort. For this reason, classroom teachers ought to be paid at least the equivalent of administrators at all levels, including the superintendent. Each
An agreement cannot bind unless both parties to the agreement know what they are doing and freely choose to do it. This implies that the seller who intends to enter a contract with a customer has a duty to disclose exactly what the customer is buying and what the terms of the sale are. Above
1. Because triangle A is congruent with triangle B, and triangle A is isosceles, it follows that triangle B is isosceles.2. The plaque on the Leaning Tower of Pisa says that Galileo performed experiments there with falling objects. It must be the case that Galileo did indeed perform those
1. Crater Lake, the deepest lake in the United States, was caused by a huge volcanic eruption 7,700 years ago. Since human beings have lived around the mountain for more than 10,000 years, it is likely that people witnessed that eruption. 2. Each element, such as hydrogen and iron, has a set of
That [the moons of Jupiter] revolve in unequal circles is manifestly deduced from the fact that at the longest elongation from Jupiter it is never possible to see two of these moons in conjunction, whereas in the vicinity of Jupiter they are found united two, three, and sometimes all four
1. Lenses function by refracting light at their surfaces. Consequently, their action depends not only on the shape of the lens surfaces, but also on the indices of refraction of the lens material and the surrounding medium. 2. Given present growth rates in underdeveloped countries, the limited
1. The Matterhorn is higher than Mount Whitney, and Mount Whitney is higher than Mount Rainier. The obvious conclusion is that the Matterhorn is higher than Mount Rainier. 2. Although both front and rear doors were found open after the burglary, there were pry marks around the lock on the rear door
Define the following terms: Deductive argument..........................Prediction Inductive argument...........................Argument from analogy Argument based on mathematics...........Generalization argument from authority Argument from definition...................Argument based on
Answer "true" or "false" to the following statements: 1. In an inductive argument, it is intended that the conclusion contain more information than the premises. 2. In a deductive argument, the conclusion is not supposed to contain more information than the premises. 3. The form of argumentation
1. Since Moby Dick was written by Shakespeare, and Moby Dick is a sciencefiction novel, it follows that Shakespeare wrote a science-fiction novel.2. Since London is north of Paris and south of Edinburgh, it follows that Paris is south of Edinburgh.3. If George Washington was beheaded, then George
1. Chicago is a city in Michigan and Michigan is part of the United States. Therefore, Chicago is a city in the United States. 2. If Queen Elizabeth was born in Los Angeles, then she is a California native. Queen Elizabeth is not a California native. Therefore, Queen Elizabeth was not born in Los
1. The grave marker at Arlington National Cemetery says that John F. Kennedy is buried there. It must be the case that Kennedy really is buried in that cemetery.2. The ebb and flow of the tides has been occurring every day for millions of years. But nothing lasts forever. Therefore, probably the
1. Since Tom is the brother of Agatha, and Agatha is the mother of Raquel, it follows that Tom is the uncle of Raquel.2. When a cook cannot recall the ingredients in a recipe, it is appropriate that she refresh her memory by consulting the recipe book. Similarly, when a student cannot recall the
Define the following terms: Valid deductive argument.....................Strong inductive argument Invalid deductive argument...................Weak inductive argument Sound argument.................................Cogent argument Unsound argument..............................Uncogent argument
Answer "true" or "false" to the following statements: 1. Some arguments, while not completely valid, are almost valid. 2. Inductive arguments allow for varying degrees of strength and weakness. 3. Invalid deductive arguments are basically the same as inductive arguments. 4. If a deductive argument
1. All galaxies are structures that contain black holes in the center, so all galaxies are quasars, since all quasars are structures that contain black holes in the center.2. Some evolutionists are not people who believe in the Bible, for no creationists are evolutionists, and some people who
1. All super PACs are unlimited spenders. For this reason, some big-time power brokers are not super PACs, inasmuch as some unlimited spenders are big-time power brokers. 2. No movie producers are uncompetitive business executives, and some Hollywood moguls are movie producers. It follows that no
1. Some improvers of humankind are not exploiters of personal information. As a result, some corporate social networks are not improvers of humankind, seeing that all corporate social networks are exploiters of personal information.2. Some drone attacks are assaults on human life, given that some
1. No patents are measures that discourage research and development, and all patents are regulations that protect intellectual property. Thus, no measures that discourage research and development are regulations that protect intellectual property. 2. Some farmworkers are not people who are paid
1. Some politicians are people who will stop at nothing to win an election, and no people who will stop at nothing to win an election are true statesmen. Hence, no politicians are true statesmen. 2. All meticulously constructed timepieces are true works of art, for all Swiss watches are true works
1. No patrons of fast-food restaurants are health-food addicts. Consequently, no patrons of fast-food restaurants are connoisseurs of fine desserts, since no connoisseurs of fine desserts are health-food addicts. 2. Some toxic dumps are sites that emit hazardous wastes, and some sites that emit
1. All persons who assist others in suicide are people guilty of murder. Accordingly, some individuals motivated by compassion are not persons guilty of murder, inasmuch as some people who assist others in suicide are individuals motivated by compassion. 2. Some school boards are not groups that
1. If animal species are fixed and immutable, then evolution is a myth. Therefore, evolution is not a myth, since animal species are not fixed and immutable. 2. If carbon dioxide is present in the atmosphere, then plants have a source of carbon. Hence, since plants have a source of carbon, carbon
1. If human rights are recognized, then civilization flourishes. If equality prevails, then civilization flourishes. Thus, if human rights are recognized, then equality prevails.2. If energy taxes are increased, then either the deficit will be reduced or conservation will be taken seriously. If the
1. All homeless people who are panhandlers are destitute individuals. Therefore, all homeless people are destitute individuals.2. Some wrestlers are colorful hulks, since some wrestlers are colorful and some wrestlers are hulks.Use the counterexample method to prove each of the following arguments
1. All community colleges with low tuition are either schools with large enrollments or institutions supported by taxes. Therefore, all community colleges are institutions supported by taxes.2. All merchandisers that are retailers are businesses that are inventory rotators. Therefore, all
1. All diabetes victims are either insulin takers or glucose eliminators. Accordingly, some diabetes victims are glucose eliminators, since some diabetes victims are insulin takers.2. All FHA loans are living-standard enhancers for the following reasons. All reverse mortgages that are FHA loans are
The following arguments were taken from magazine and newspaper editorials and letters to the editor. In most instances the main conclusion must be rephrased to capture the full intent of the author. Write out what you interpret the main conclusion to be.1. University administrators know well the
1. (1) The conditions under which many food animals are raised are unhealthy for humans. (2) To keep these animals alive, large quantities of drugs must be administered. (3) These drugs remain in the animals' flesh and are passed on to the humans who eat it. 2. (1) The development of
1. (1) There is a lot of pressure on untenured college teachers to dumb down their courses. (2) Administrators tend to rehire teachers who bring in more money, and (3) teachers who dumb down their classes do precisely this. Why? Because (4) easier classes attract more students, and (5) more
1. (1) Numerous cancer patients on chemotherapy suffer from constant nausea, loss of appetite, and inability to sleep. (2) For many of these patients, inhaled marijuana is the only medicine that provides relief. (3) Also, it causes no harmful side effects. (4) For these reasons, medical marijuana
1. (1) When parents become old and destitute, the obligation of caring for them should be imposed on their children. (2) Clearly, children owe a debt to their parents. (3) Their parents brought them into the world and cared for them when they were unable to care for themselves. (4) This debt could
1. (1) It appears that animals may be able to predict earthquakes. (2) Prior to a major quake in China, hundreds of snakes suddenly appeared from hibernation and froze to death in the snow, (3) fish were seen leaping from rivers and lakes, and (4) cows and horses refused to enter barns. Also, (5)
1. (1) Many people believe that the crime of bribery cannot extend to campaign contributions. (2) From a legal standpoint, however, countless campaign contributions are in fact bribes. (3) A bribe is anything of value or advantage given with the intent to unlawfully influence the person to whom it
1. (1) It has been widely acknowledged that the quality of undergraduate education in this country is diminishing. (2) An often unrecognized cause of this malady is the exploitative way that universities as employers treat their parttime and temporary faculty members. (3) In many universities there
1. (1) The state has a right to intervene on behalf of unborn children, and (2) this right should be implemented immediately. (3) While it may be true that a mere fetus has no rights, (4) surely a born child does have rights, and (5) these rights project backward to the time it was in the womb.
1. (1) Powerful new particle accelerators are important in high-energy physics, and (2) they are worth their cost because (3) they will allow scientists to produce and capture significant quantities of Z particles. (4) Z particles result from the collision of positrons and electrons, and (5)
1. (1) Cigarette consumption could be easily reduced by simply outlawing tailormade cigarettes. (2) The manufacture of tailor-made cigarettes to American standards is a high-tech industry. (3) It cannot be done in small illicit labs like the processing of PCP, cocaine, or heroin. (4) The
Define the following terms: Logic........................Premise........................Inference Argument...................Conclusion.....................Proposition Statement...................Conclusion indicator.........Syllogistic logic Truth value..................Premise

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A Concise Introduction to Logic 13th edition Patrick J. Hurley, Lori Watson - Solutions

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