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logic functions and equations

A Concise Introduction To Logic 11th Edition Patrick J. Hurley - Solutions

7. True Or False. A sound argument may be invalid.
6. True Or False. A valid argument may have a false premise and a true conclusion.
5. True Or False. A valid argument may have a false premise and a false conclusion.
4. True Or False. If a deductive argument has true premises and a false conclusion, it is necessarily invalid.
3. True Or False. Invalid deductive arguments are basically the same as inductive arguments.
2. True Or False. Inductive arguments admit of varying degrees of strength and weakness.
1. True Or False. Some arguments, while not completely valid, are almost valid.
21. Defi ne the following terms: valid argument invalid argument sound argument unsound argument strong argument weak argument cogent argument uncogent argument
20. Since Michael is a Pisces, it necessarily follows that he was born in March. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive, determine whether it is valid or invalid.
★19. Statistics reveal that 86 percent of those who receive fl u shots do not get the fl u. Jack received a fl u shot one month ago. Th erefore, he should be immune, even though the fl u is going around now. Determine whether the following arguments are inductive or deductive. If an argument is
18. If infl ation heats up, then interest rates will rise. If interest rates rise, then 1 bond prices will decline. Th erefore, if infl ation heats up, then bond prices will decline. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether
17. If acupuncture is hocus pocus, then acupuncture cannot relieve chronic pain.But acupuncture can relieve chronic pain. Therefore, acupuncture is not hocus pocus. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or
★16. Since x + y = 10, and x = 7, it follows that y = 4. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive, determine whether it is valid or invalid.
15. Harry will never be able to solve that diffi cult problem in advanced calculus in the limited time allowed. He has never studied anything beyond algebra, and in that he earned only a C–. Determine whether the following arguments are inductive or deductive. If an argument is inductive,
14. Th e Japanese attack on Pearl Harbor happened in either 1941 or 1951. But it didn’t happen in 1941. Th erefore, it happened in 1951. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive,
★13. Th is cash register drawer contains over 100 coins. Th ree coins selected at random were found to have dates earlier than 1960. Th erefore, probably all of the coins in the drawer have dates earlier than 1960. Determine whether the following arguments are inductive or deductive. If an
12. Since John loves Nancy and Nancy loves Peter, it follows necessarily that John loves Peter. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive, determine whether it is valid or invalid.
11. Robert has lost consistently at blackjack every day for the past several days.Th erefore, it is very likely that he will win today. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive,
★10. Circle A has exactly twice the diameter of circle B. From this we may conclude that circle A has exactly twice the area of circle B. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive,
9. Th e picnic scheduled in the park for tomorrow will most likely be cancelled.It’s been snowing for six days straight. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive, determine whether
8. Since Phyllis is the cousin of Denise, and Denise is the cousin of Harriet, it follows necessarily that Harriet is the cousin of Phyllis. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive,
★7. Aft er taking LSD, Alice said she saw a fl ying saucer land in the shopping center parking lot. Since Alice has a reputation for always telling the truth, we must conclude that a fl ying saucer really did land there. Determine whether the following arguments are inductive or deductive. If an
6. By accident Karen baked her brownies two hours longer than she should have. Th erefore, they have probably been ruined. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive, determine whether
5. Suppose fi gure A is a triangle having two equal angles. It follows that fi gure A has two equal sides. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive, determine whether it is valid or
★4. Since Christmas is always on a Th ursday, it follows that the day aft er Christmas is always a Friday. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive, determine whether it is valid
3. Th e Broadway Th eater marquee says that Th e Phantom of the Opera is playing nightly. Th erefore, it must be that case that Phantom is playing there tonight. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or
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 answers during a fi nal exam, it is appropriate that she refresh her memory by consulting the textbook. Determine
★1. Since Tom is the brother of Agatha, and Agatha is the mother of Raquel, it follows that Tom is the uncle of Raquel. Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive, determine whether
15. A random sample of twenty-fi ve famous country and western singers, including Garth Brooks and Dolly Parton, revealed that every single one of them studied music in Tasmania. Th erefore, probably the majority of famous country and western singers studied music in Tasmania. The following
14. Unlike monkeys, today’s humans have feet that are not suited for grasping objects. Therefore, a thousand years from now, probably humans will still have feet that are not suited for grasping objects. The following arguments are inductive. Determine whether each is strong or weak, and note the
★13. The African American athlete Adrian Peterson is able to withstand tremendous impacts on the football field. However, Serena Williams, like Adrian Peterson, is a great African American athlete. Therefore, Serena Williams should be able to withstand tremendous impacts on the football field.
12. When Neil Armstrong landed on the moon, he left behind a gold-plated Schwinn bicycle, which he used to ride around on the moon’s surface.Probably that bicycle is still up there on the moon. The following arguments are inductive. Determine whether each is strong or weak, and note the
11. Every map of the United States shows that Alabama is situated on the Pacifi c coast. Th erefore, Alabama must be a western state. The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and the truth or falsity of the
★10. Coca-Cola is an extremely popular soft drink. Th erefore, probably someone, somewhere, is drinking a Coke right this minute. The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and the truth or falsity of the
9. The Declaration of Independence says that all men are endowed by their creator with certain unalienable rights. Th erefore it probably follows that a creator exists. The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and
8. Paleontologists have unearthed the fossilized bones of huge reptiles, which we have named dinosaurs. Tests indicate that these bones are more than 50 million years old. Th erefore, probably dinosaurs really did roam the earth 50 million years ago. The following arguments are inductive. Determine
★7. People have been listening to rock and roll music for over a hundred years.Probably people will still be listening to it a year from now. The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and the truth or falsity of
6. Constructing the great pyramid at Giza required lift ing massive stone blocks to great heights. Probably the ancient Egyptians had some antigravity device to accomplish this feat. The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between
5. Most popular film stars are millionaires. Ellen Page is a popular film star.Th erefore, probably Ellen Page is a millionaire. The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and the truth or falsity of the premise(s)
★4. Franklin Delano Roosevelt said that we have nothing to fear but fear itself.Th erefore, women have no reason to fear serial rapists. The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and the truth or falsity of the
3. Th e vast majority of Rose Bowl games (in Pasadena, California) have been played in freezing cold weather. Th erefore, probably the next Rose Bowl game will be played in freezing cold weather. The following arguments are inductive. Determine whether each is strong or weak, and note the
2. The ebb and flow of the tides has been occurring every day for millions of 1 years. But nothing lasts forever. Th erefore, probably the motion of the tides will die out within a few years. The following arguments are inductive. Determine whether each is strong or weak, and note the relationship
★1. Th e 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. The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and
15. Th e United States Congress has more members than there are days in the year.Th erefore, at least two members of Congress have the same birthday. The following arguments are deductive. Determine whether each is valid or invalid, and note the relationship between your answer and the truth or
14. All physicians are individuals who have earned degrees in political science, and some lawyers are physicians. Th erefore, some lawyers are persons who have earned degrees in political science. The following arguments are deductive. Determine whether each is valid or invalid, and note the
★13. Since some fruits are green, and some fruits are apples, it follows that some fruits are green apples. The following arguments are deductive. Determine whether each is valid or invalid, and note the relationship between your answer and the truth or falsity of the premises and conclusion.
12. Since Winston Churchill was English, and Winston Churchill was a famous statesman, we may conclude that at least one Englishman was a famous statesman. The following arguments are deductive. Determine whether each is valid or invalid, and note the relationship between your answer and the truth
11. Since the Department of Defense Building outside Washington, D.C., has the shape of a hexagon, it follows that it has seven sides. The following arguments are deductive. Determine whether each is valid or invalid, and note the relationship between your answer and the truth or falsity of the
★10. Every province in Canada has exactly one city as its capital. Therefore, since there are thirty provinces in Canada, there are thirty provincial capitals. The following arguments are deductive. Determine whether each is valid or invalid, and note the relationship between your answer and the
9. If President Barack Obama was born in Massachusetts, then he is a native of New England. Barack Obama is not a native of New England. Th erefore, Barack Obama was not born in Massachusetts. The following arguments are deductive. Determine whether each is valid or invalid, and note the
8. Chicago is a city in Michigan and Michigan is part of the United States.Th erefore, Chicago is a city in the United States. The following arguments are deductive. Determine whether each is valid or invalid, and note the relationship between your answer and the truth or falsity of the premises
★7. All leopards with lungs are carnivores. Th erefore, all leopards are carnivores. The following arguments are deductive. Determine whether each is valid or invalid, and note the relationship between your answer and the truth or falsity of the premises and conclusion. Finally, determine whether
6. Th e Empire State Building is taller than the Statue of Liberty, and the Statue of Liberty is taller than the Eiff el Tower. Th erefore, the Empire State Building is taller than the Eiff el Tower. The following arguments are deductive. Determine whether each is valid or invalid, and note the
5. Since the Spanish-American War occurred before the U.S. Civil War, and the U.S. Civil War occurred aft er the Korean War, it follows that the Spanish-American War occurred before the Korean War. The following arguments are deductive. Determine whether each is valid or invalid, and note the
★4. The longest river in South America is the Amazon, and the Amazon flows through Brazil. Th erefore, the longest river in South America fl ows through Brazil. The following arguments are deductive. Determine whether each is valid or invalid, and note the relationship between your answer and the
3. If George Washington was beheaded, then George Washington died. George Washington died. Th erefore, George Washington was beheaded. The following arguments are deductive. Determine whether each is valid or invalid, and note the relationship between your answer and the truth or falsity of the
2. Since London is north of Paris and south of Edinburgh, it follows that Paris is south of Edinburgh. The following arguments are deductive. Determine whether each is valid or invalid, and note the relationship between your answer and the truth or falsity of the premises and conclusion. Finally,
★1. Since Moby Dick was written by Shakespeare, and Moby Dick is a science fi ction novel, it follows that Shakespeare wrote a science fi ction novel. The following arguments are deductive. Determine whether each is valid or invalid, and note the relationship between your answer and the truth or
15. True or False Deductive arguments always proceed from the general to the particular.
14. True or False Inductive arguments always proceed from the particular to the general.
13. True or False An argument that predicts what will happen in the future, based on what has happened in the past, is an inductive argument.
12. True or False If an argument contains the phrase “it defi nitely follows that,” then we know for certain that the argument is deductive.
11. True or False An argument that proceeds from knowledge of a cause to knowledge of an eff ect is an inductive argument.
10. True or False An argument that presents two alternatives and eliminates one, leaving the other as the conclusion, is an inductive argument.
9. True or False An argument that draws a conclusion that something is true because someone has said that it is, is a deductive argument.
8. True or False An argument that draws a conclusion about a thing based on that thing’s similarity to something else is a deductive argument.
7. True or False If the conclusion of an argument follows merely from the defi nition of a word used in a premise, the argument is deductive.
6. True or False Most arguments based on statistical reasoning are deductive.
5. True or False A geometrical proof is an example of an inductive argument.
4. True or False Th e actual strength of the link between premises and conclusion may allow one to determine whether an argument is inductive or deductive.
3. True or False The form of argumentation the arguer uses may allow one to determine whether an argument is inductive or deductive.
2. True or False In a deductive argument, the conclusion is not supposed to contain more information than the premises.
1. In an inductive argument, it is intended that the conclusion contain more information than the premises. True or False
31. Defi ne the following terms: deductive argument inductive argument argument based on mathematics argument from definition categorical syllogism hypothetical syllogism disjunctive syllogism argument from analogy generalization prediction argument from authority argument based on signs causal
30. Because the moon moves relative to the earth so that it returns to the same position overhead aft er about 25 hours, there are two high and two low tides at any point every 25 hours.Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the
29. We tell people not to speed, but equip cars with air bags in case they do. So what’s wrong with telling kids not to have sex, but making Plan B available in case they do?Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the criteria you
★28. Animals that live on plant foods must eat large quantities of vegetation, and 1 this consumes much of their time. Meat eaters, by contrast, have no need to eat so much or so often. Consequently, meat-eating hominines [early humans] may have had more leisure time available to explore and
27. Ordinary things that we encounter every day are electrically neutral. Th erefore, since negatively charged electrons are a part of everything, positively charged particles must also exist in all matter.Determine whether the following arguments are best interpreted as being inductive or
26. Eternity is simultaneously whole. But time has a before and an aft er. Th erefore time and eternity are not the same thing.Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the criteria you use in reaching your decision (i.e., the
★25. Th e Simpson incident had shown me that a dog was kept in the stables, and yet, though someone had been in and had fetched out a horse, he had not barked enough to arouse the two lads in the loft . Obviously the midnight visitor was someone whom the dog knew well.Determine whether the
24. The interpretation of the laws is the proper and peculiar province of the courts. A constitution is, in fact, and must be regarded by the judges, as a fundamental law. It therefore belongs to them to ascertain its meaning, as well as the meaning of any particular act proceeding from the
23. Given present growth rates in underdeveloped countries, the limited practice of birth control, and the diffi culty of slowing the current growth momentum, it can be said with virtual certainty that none of the people now reading this book will ever live in a world where the population is not
★22. 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.Determine whether the following arguments are best interpreted as being
21. Th at [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
20. Th e graphical method for solving a system of equations is an approximation, since reading the point of intersection depends on the accuracy with which the lines are drawn and on the ability to interpret the coordinates of the point.Determine whether the following arguments are best interpreted
★19. When the Romans occupied England, coal was burned. Since coal produces quite a bit of soot and sulfur dioxide, there must have been days almost 2000 years ago when the air in the larger towns was badly polluted.Determine whether the following arguments are best interpreted as being inductive
18. Reserves of coal in the United States have an energy equivalent 33 times that of oil and natural gas. On a worldwide basis the multiple is about 10. By shift -ing to a coal-based economy, we could satisfy our energy requirements for at least a century, probably longer.Determine whether the
17. Because the apparent daily movement which is common to both the planets and the fi xed stars is seen to travel from the east to the west, but the far slower single movements of the single planets travel in the opposite direction from west to east, it is therefore certain that these movements
★16. Each element, such as hydrogen and iron, has a set of gaps—wavelengths that it absorbs rather than radiates. So if those wavelengths are missing from the spectrum, you know that that element is present in the star you are observing.Determine whether the following arguments are best
15. Crater Lake, the deepest lake in the United States, was caused by a huge volcanic eruption 7700 years ago. Since human beings have lived around the mountain for more than 10,000 years, it is likely that people witnessed that eruption.Determine whether the following arguments are best
14. If Alexander the Great died from typhoid fever, then he became infected in India. Alexander the Great did die from typhoid fever. Th erefore, he became infected in India. Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the criteria you
★13. World-renowned physicist Stephen Hawking says that the condition of the universe at the instant of the Big Bang was more highly ordered than it is today. In view of Hawking’s stature in the scientifi c community, we should conclude that this description of the universe is correct.
12. Either classical culture originated in Greece, or it originated in Egypt. Classical culture did not originate in Egypt. Th erefore, classical culture originated in Greece. Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the criteria you
11. Cholesterol is endogenous with humans. Th erefore, it is manufactured inside the human body. Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the criteria you use in reaching your decision (i.e., the presence of indicator words, the
★10. Th e Encylopaedia Britannica has an article on symbiosis. Th e Encyclopedia Americana, like the Britannica, is an excellent reference work. Th erefore, the Americana probably also has an article on symbiosis. Determine whether the following arguments are best interpreted as being inductive
9. Although both front and rear doors were found open aft er the burglary, there were pry marks around the lock on the rear door and deposits of mud near the threshold. It must be the case that the thief entered through the rear door and left through the front. Determine whether the following
8. Th e Matterhorn is higher than Mount Whitney, and Mount Whitney is higher 1 than Mount Rainier. Th e obvious conclusion is that the Matterhorn is higher than Mount Rainier. Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the criteria you
★7. Paying off terrorists in exchange for hostages is not a wise policy, since such action will only lead them to take more hostages in the future.Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the criteria you use in reaching your
6. Th e longer a pendulum is, the longer it takes to swing. Th erefore, when the pendulum of a clock is lengthened, the clock slows down.Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the criteria you use in reaching your decision (i.e.,
5. Amoco, Exxon, and Texaco are all listed on the New York Stock Exchange. It must be the case that all major American oil companies are listed on the New York Stock Exchange.Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the criteria you

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