Exam (elaborations) Instructor’s Manual_Test Bank for THE LOGIC BOOK 4th Edition MERRIE BERGMANN, JAMES MOOR and JACK NELSON The Logic Book, ISBN: 9780072401899

Exam (elaborations) Instructor’s Manual_Test Bank for THE LOGIC BOOK 4th Edition MERRIE BERGMANN, JAMES MOOR and JACK NELSON The Logic Book, ISBN: 1899 CONTENTS Overview iv The Option of a Self-Paced Course v TESTS AND ANSWERS Chapter 1 1 Chapter 2 13 Chapter 3 25 Chapter 4 35 Chapter 5 45 Chapter 6 No tests Chapter 7 58 Chapter 8 70 Chapter 9 79 Chapter 10 92 Chapter 11 No tests SOLUTIONS TO EXERCISES Chapter 1 1 Chapter 2 9 Chapter 3 18 Chapter 4 39 Chapter 5 89 Chapter 6 133 Chapter 7 137 Chapter 8 147 Chapter 9 178 Chapter 10 239 Chapter 11 283 INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK 1 TESTS AND ANSWERS CHAPTER ONE LOGIC TEST 1 1. Define the following: a. Logical truth b. Deductive validity c. Logical equivalence 2. For each of the following, indicate whether it has a truth-value (i.e., is either true or false). If it does not, explain why not. a. Mars is the planet closest to the sun. b. May you inherit a hotel and die in every room. c. Police cars use left lane. d. Ask not for whom the bell tolls. 3. Which of the following passages are best understood as arguments? For those that are, recast the passage in standard form and determine whether the resulting argument is deductively valid. Evaluate the inductive strength of those that are not deductively valid. a. That boxer cannot be hurt too badly because he is still moving well and throwing hard punches. b. One should not open the bidding with a five-point bridge hand. 2 INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK c. Either the members of the electoral college do their job or they don’t. Thus the members of the electoral college are either useless or dangerous, for if they do their job, they are useless, and if they don’t, they are dangerous. 4. For each of the following, circle T if the sentence is true or F if the sentence is false. T F a. A set all of whose members are true is logically consistent. T F b. All valid arguments have true conclusions. T F c. Every sound argument is deductively valid. T F d. Every argument that has inductive strength is also deductively valid. T F e. A sound argument is a valid argument with a true conclusion. 5. Give an example of each of the following where one exists. If there can be no such example, explain why. a. A valid argument that has true premises and a true conclusion. b. A sound argument with a false conclusion. c. A consistent set all of whose members are false. ANSWERS 1. a. A sentence is logically true if and only if it is not possible for the sentence to be false. b. An argument is deductively valid if and only if it is not possible for the premises to be true and the conclusion false. An argument is deductively invalid if and only if it is not deductively valid. c. The members of a pair of sentences are logically equivalent if and only if it is not possible for one of the sentences to be true while the other sentence is false. 2. a. This sentence does have a truth-value (as it happens, the value ‘false’). b. This sentence is a curse. It has no truth-value. c. This marginally grammatical sentence might be an instruction to police officers, in which case it does not have a truth-value. It might also be a warning to motorists, in which case it does have a truth-value. d. This is a bit of advice. It has no truth-value. 3. a. There is an argument here: That boxer is moving well and throwing hard punches. That boxer cannot be hurt too badly. The argument is deductively invalid. (The boxer may have injuries that are not apparent.) It does have considerable inductive strength. b. This is not an argument. It is a claim, probably a true one, that certain behavior in bridge is inadvisable. c. This is an argument: INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK 3 Either the members of the electoral college do their job or they don’t. If the members of the electoral college do their job, then they are useless. If the members of the electoral college don’t do their job, then they are dangerous. The members of the electoral college are either useless or dangerous. This argument is deductively valid. It is not possible for the premises to be true and the conclusion false. 4. a. T b. F A valid argument can have a false conclusion so long as at least one of its premises is also false. Here is an example: The largest city in each state is the capital of that state. Los Angeles is the largest city in California. Los Angeles is the capital of California. The first premise and the conclusion of this argument are both false. c. T d. F Many arguments with some degree of inductive strength are deductively invalid. See, for example, the above argument concerning a boxer. e. F Sound arguments do have true conclusions, but not all valid arguments with true conclusions are sound, for not all such arguments have true premises. An example is The largest city in each state is the capital of that state. Denver is the largest city in Colorado. Denver is the capital of Colorado. This argument is valid and it has a true conclusion, but it is not sound. 5. a. A valid argument that has true premises and a true conclusion: Honolulu is the largest city in Hawaii and the capital of Hawaii. Honolulu is the capital of Hawaii. b. A sound argument with a false conclusion: There can be no such argument, for a sound argument is by definition a valid argument with true premises, and a valid argument is one where it is impossible for the premises to be true and the conclusion false. c. A consistent set all of whose members are false: {Los Angeles is the capital of California, Miami is the capital of Florida} 4 INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK LOGIC TEST 2 1. Define the following: a. Logical indeterminacy b. Deductive soundness c. Logical consistency 2. For each of the following, indicate whether it has a truth-value (i.e., is either true or false). If it does not, explain why not. a. Count no man lucky until he is dead. b. Whenever a general runs for President, he or she gets elected. c. I promise to be on time for class. d. There once was a barber of Seville who shaved all and only those citizens of Seville who shaved but did not shave themselves. 3. Which of the following passages are best understood as arguments? For those that are, recast the passage in standard form and determine whether the resulting argument is deductively valid. Evaluate the inductive strength of those that are not deductively valid. a. This ship is going to sink. She has been holed in three places and the pumps aren’t working. No ship with that kind of damage can stay afloat. b. Black clouds are moving in and the barometer is dropping rapidly, so there is a storm coming. c. Truman was elected because he had experience, Eisenhower because he was a war hero, Kennedy because he was young, and Nixon for no reason at all. 4. For each of the following, circle T if the sentence is true or F if the sentence is false. T F a. Every argument whose conclusion is logically true is valid. T F b. Every argument with true premises and a true conclusion is valid. T F c. Every sound argument has a true conclusion. T F d. As explicated in Chapter 1, the term ‘sound’ applies to both arguments and sentences. T F e. Every pair of true sentences is a pair of logically equivalent sentences. 5. Give an example of each of the following where one exists. If there can be no such example, explain why. a. A valid argument with at least one false premise and a true conclusion. b. An invalid argument with true premises and a true conclusion. c. A consistent set containing at least one logically false sentence. ANSWERS 1. a. A sentence is logically indeterminate if and only if it is neither logically true nor logically false. INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK 5 b. An argument is deductively sound if and only if it is deductively valid and all of its premises are true. An argument is deductively unsound if and only if it is not deductively sound. c. A set of sentences is logically consistent if and only if it is possible for all the members of that set to be true at the same time. A set of sentences is logically inconsistent if and only if it is not logically consistent. 2. a. This sentence does not have a truth-value. It is an ancient Greek adage that, grammatically, is an instruction or command. b. This sentence does have a truth-value. (It is false. George B. McClellan ran for President in 1864 and lost to Lincoln.) c. Whenever this sentence is said or written, in a normal context, it thereby becomes true. So it does have a truth-value. (Sentences of this sort, which cannot be said falsely, are called performatives.) d. This sentence does have a truth-value: It may be either true or false. That is, we do not know whether there had been such a barber, but we do know that if such a barber existed, he or she was a person who did not shave. 3. a. There is an argument here: This ship has been holed in three places and the pumps aren’t working. No ship that has been holed in three places and whose pumps are not working can stay afloat. This ship is going to sink. This argument is deductively valid. It is impossible for the premises to be true and the conclusion false. b. There is an argument here: Black clouds are moving in and the barometer is dropping rapidly. There is a storm coming. This argument is not deductively valid. It is possible that the premise is true but that a storm will not materialize. However, the argument does have inductive strength. Black clouds and a falling barometer are indicators of a coming storm. c. There is no argument here. The passage is best construed as a commentary on the American political system. 4. a. T b. F Many such arguments are invalid. Here is an example: Kennedy was President and a Democrat. Roosevelt was President and a Democrat. Carter was President and a Democrat. Clinton is President. Clinton is a Democrat. 6 INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK It is possible for the premises of this argument to be true and the conclusion false. This would be the case were Clinton to change his party affiliation and become a Republican. Note that the premises do not negate this possibility. c. T d. F The term sound applies only to arguments. e. F The sentences ‘Clinton defeated Bush’ and ‘Reagan defeated Carter’ are both true, but this alone does not make them logically equivalent. It is possible for one of them to be true and the other false. For example, had Carter succeeded in rescuing the hostages in Iran he might have defeated Reagan, in which case ‘Clinton defeated Bush’ would be true and ‘Reagan defeated Carter’ false. 5. a. Anchorage is the capital of Alaska and Anchorage is a seaport. The capital of Alaska is a seaport. The premise is false: Juneau, not Anchorage, is the capital of Alaska. But Juneau is a seaport, so the conclusion is true. Therefore the argument is valid, for it is impossible for the premise to be true and the conclusion false. b. Some women are lawyers. Some lawyers are dishonest. Some women are dishonest. The premises and the conclusion are all true, but the argument is deductively invalid. It is possible for the premises to be true but the conclusion false: This would be the case if all women were honest (and accordingly the only lawyers who are dishonest would be males). c. There can be no such set. If a sentence is logically false, then it cannot be true. Therefore not all the members of a set that has that sentence as a member can be true, so such a set must be inconsistent. LOGIC TEST 3 1. Define the following: a. Argument b. Logical falsity c. Deductive validity 2. For each of the following, indicate whether it has a truth-value (i.e., is either true or false). If it does not, explain why not. a. Who’s in charge here anyway? b. No pain, no gain. c. Never look a gift horse in the mouth. d. Sentence 2.c. is true. INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK 7 3. Which of the following passages are best understood as arguments? For those that are, recast the passage in standard form and determine whether the resulting argument is deductively valid. Evaluate the inductive strength of those that are not deductively valid. a. The stock market has risen dramatically, but wages have not. Whenever the stock market rises, the upper class benefits. Whenever wages are flat, the lower and middle classes are hurt. So if the present trend continues, the social fabric of the country will suffer. b. FDR was a Democrat and didn’t balance the budget. Kennedy was a Democrat and didn’t balance the budget. Carter was a Democrat and didn’t balance the budget. Clinton is a Democrat. So the budget won’t be balanced during Clinton’s administration. c. War is too important to leave to the generals and peace is too important to leave to the politicians. 4. For each of the following, circle T if the sentence is true of F if the sentence is false. T F a. Every pair of logically true sentences is a pair of logically equivalent sentences. T F b. Every argument has two premises and one conclusion. T F c. Every set that contains at least one false sentence is logically inconsistent. T F d. Every valid argument has a true conclusion. T F e. If a set is consistent then every member of the set is true. 5. Give an example of each of the following where one exists. If there can be no such example, explain why. a. A valid argument with a logically false conclusion. b. An inconsistent set at least one member of which is logically true. c. A sentence that is neither logically true, nor logically false, nor logically indeterminate. ANSWERS 1. a. An argument is a set of sentences one of which (the conclusion) is taken to be supported by the remaining sentences (the premises). b. A sentence is logically false if and only if it is not possible for the sentence to be true. c. An argument is deductively valid if and only if it is not possible for the premises to be true and the conclusion false. 2. a. This sentence is a question, hence it is neither true nor false. b. This sentence is short for something like ‘If there is no pain involved, then there is no gain to be had’ and as such does have a truth-value. 8 INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK c. This sentence is an imperative or command. It gives instructions, not information. Hence it is neither true nor false. d. This sentence says, falsely, that the preceding sentence is true. Therefore it does have a truth-value (false). 3. a. There is an argument here: The stock market has risen dramatically, but wages have not Whenever the stock market rises, the upper class benefits. Whenever wages are flat, the lower and middle classes are hurt. If the present trend continues, the social fabric of the country will suffer. The argument is deductively invalid, for no explicit connection is given between the upper classes benefiting, the lower and middle classes being hurt, and the social fabric of the country suffering. However, the argument does have considerable inductive strength. It is probable that the social fabric of the country will suffer if the lower and middle classes are hurt while the upper class benefits. b. There is an argument here: FDR was a Democrat and didn’t balance the budget. Kennedy was a Democrat and didn’t balance the budget. Carter was a Democrat and didn’t balance the budget. Clinton is a Democrat. The budget won’t be balanced during Clinton’s administration. The argument is deductively invalid. Even though Democratic Presidents of the recent past have not balanced the budget, it is possible that Clinton will be different, that he will balance the budget. The argument does have some inductive strength. That recent Democratic Presidents have not balanced the budget, together with the fact that Clinton is a Democrat, gives some reason to believe that Clinton will not balance the budget. c. There is no argument here. This sentence makes two claims: one about war and generals, the other about peace and politicians. 4. a. T b. F All arguments do have one conclusion, but they can have any number of premises. c. F The set whose only members are ‘Ford succeeded Nixon’ and ‘Bush defeated Clinton’ contains two sentences, one of which is false. But the set is not inconsistent. It is possible, had history gone other than it did, that Bush defeated Clinton. So it is possible that all the members of this set are true, and hence the set is consistent. INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK 9 d. F In a valid argument, the conclusion must be true if the premises are all true, but if one or more premises is false, the conclusion may also be false. For example: Every president elected in the 20th century has been a Democrat. Reagan was elected in the 20th century. Reagan was a Democrat This is a valid argument with one false premise and a false conclusion. e. F The set given in the answer to 4.c above is consistent, but has one false member. 5. a. Everyone in the class will pass and someone in the class will not pass. The final will, and will not, be given on Friday. The conclusion of this argument is logically false, but so is the premise. Therefore it is impossible for the premise to be true, and thus impossible for the premise to be true and the conclusion false. So the argument is deductively valid. b. Consider the set whose three members are ‘Samantha will graduate’, ‘Samantha will not graduate’, and ‘Either Samantha will graduate or she will not graduate’. The last listed member is logically true, but the set is inconsistent, for it is impossible for both the first and second listed members to be true at the same time. c. This text is devoted to the study of the relations among sentences that are either true or false, and each such sentence is either logically true, logically false, or logically indeterminate. But there are sentences falling outside the purview of this text—for example questions and commands—that are neither true nor false and hence neither logically true, nor logically false, nor logically indeterminate. One such sentence is ‘Who thought up this exercise anyway?’ LOGIC TEST 4 1. Define the following: a. Inductive strength b. Logical consistency c. Logical indeterminacy 2. For each of the following, indicate whether it has a truth-value (i.e., is either true or false). If it does not, explain why not. a. Abandon hope all ye who enter here. b. This sentence is false. c. 2 is the smallest prime number. d. Who made up this test anyway? 10 INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK 3. Which of the following passages are best understood as arguments? For those that are, recast the passage in standard form and determine whether the resulting argument is deductively valid. Evaluate the inductive strength of those that are not deductively valid. a. The demand for Ph.D.s in engineering is down. The production of Ph.D.s in engineering is up. So there are more Ph.D.s in engineering than there is demand. b. If it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic. c. When all is said and done, there will be no more to say or do. 4. For each of the following, circle T if the sentence is true or F if the sentence is false. T F a. If the members of a pair of sentences are logically equivalent, then either both are logically true, or both are logically false, or both are logically indeterminate. T F b. An argument whose conclusion is logically equivalent to one of its premises is logically valid. T F c. Every logically inconsistent set contains at least one logically false sentence. T F d. An argument can be deductively sound without being deductively valid. T F e. Every argument has two premises and one conclusion. 5. Give an example of each of the following where one exists. If there can be no such example, explain why. a. A pair of logically indeterminate sentences that are logically equivalent. b. A pair of sentences both of which are logically indeterminate but that are not logically equivalent. c. A valid argument whose conclusion is logically false and no premise of which is logically false. ANSWERS 1. a. An argument has inductive strength to the extent that the conclusion is probable given the premises. b. A set of sentences is logically consistent if and only if it is possible for all the members of that set to be true at the same time. A set of sentences is logically inconsistent if and only if it is not logically consistent. c. A sentence is logically indeterminate if and only if it is neither logically true nor logically false. 2. a. This sentence does not have a truth-value. It is an instruction, or bit of advice. (It is the sentence written over the gate to Hell in Dante’s Inferno.) b. This sentence might appear to have a truth-value, but it does not. INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK 11 Were sentence b true, then what it says, that sentence b is false, would be false. That is, were sentence b true it would also have to be false. And were sentence b false, then what sentence b says (that sentence b is false) would be true. That is, were sentence b false it would also have to be true. No sentence can be both true and false, so sentence b must be neither true nor false. The apparent paradox embodied by sentence b is brought about by the reference of that sentence to itself. To avoid paradox, logicians generally disallow this sort of self-reference. c. This sentence is true. (In mathematics, by definition 1 is not a prime number.) d. This sentence is a question and as such is neither true nor false. 3. a. There is an argument here: The demand for Ph.D.s in engineering is down. The production of Ph.D.s in engineering is up. There are more Ph.D.s in engineering than there is demand for. The argument is not deductively valid. To see this, note that in the past the demand for Ph.D.s in engineering may have been enormously greater than the supply. If so, then even if the demand is down and the supply up, the demand may still be greater than the supply. In the absence of information about the past relation of supply to demand, the argument also has little inductive strength. b. This passage, from Lewis Carroll’s Through the Looking Glass, can be construed as the following argument plus the comment ‘That’s logic’. If it was so, it might be. If it were so, it would be. It isn’t It ain’t. The conclusion, ‘It ain’t’, is colloquial for ‘It is not’, and does follow from the third premise alone. So the argument is deductively valid. c. There is no argument here. The sentence ‘When all is said and done, there will be no more to say or do’ is, however, logically true. 4. a. T b. T In such an argument, it is impossible for all the premises to be true and the conclusion false, for if the conclusion is false, so is the premise to which it is logically equivalent. c. F The set whose only two members are the sentences ‘The President is a Democrat’ and ‘The President is not a Democrat’ is logically inconsistent (both members cannot be true at the same time), but no member is logically false (both are logically indeterminate). d. F A deductively sound argument is, by definition, a deductively valid argument with true premises. 12 INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK e. F Every Aristotelean syllogism has two premises and one conclusion, but not every argument is an Aristotelean syllogism. In fact, while every argument has one and only one conclusion, an argument may have any (finite) number of premises. 5. a. One such pair consists of ‘Alice and Irene both got As’ and ‘Irene and Alice both got A’s’. b. One such pair consists of ‘Alice got an A’ and ‘Irene got an A’. c. One such argument is The President is a Democrat. The President is not a Democrat. Whatever will be won’t be. INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK 13 CHAPTER TWO LOGIC TEST 1 1. Give a truth-functional paraphrase of each of the following. Symbolize each paraphrase in SL, being sure to indicate which sentences your sentence letters abbreviate. a. I won’t go to Boston unless it rains, although Bill will go if and only if his car is running. b. Mares eat oats and bears eat oats and little lambs eat ivy. c. William fancied that leprechauns or poltergeists were persecuting him. d. Michael Crichton is one of the most creative people alive, and, if he tries his hand at television, he’ll be a success. e. Two heads aren’t better than one. 2. Give a truth-functional paraphrase of the following argument, and put it into standard form. Symbolize the paraphrased argument in SL, indicating which sentences your sentence letters abbreviate. Unless the local bookstore carries novels by Mishima, I won’t be able to complete my bibliography. None of Mishima’s novels is in the library, and, if there aren’t any there, there won’t be any in the bookstore either. If I don’t complete my bibliography, I can’t go home this weekend or next. So I can’t go home next weekend. 3. Give the chracteristic truth-tables for the following connectives: P ∼ P P Q P& Q P∨Q P⊃Q P
Q T T T F T F F T F F 4. Assuming that ‘A’ has the truth-value T and ‘B’ has the truth-value F, what is the truth-value of each of the following sentences? a. A
B b. B ∨ B c. B ⊃ A d. ∼ A e. B & A 14 INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK 5. Use the following abbreviations to give clear, idiomatic English readings for a–c. R: The race track is muddy. B: Bright Horse is the favorite. G: The odds on Bright Horse are good. C: The odds on Cinch Bet are good. a. (C
B) & ∼ G b. [(∼ B ∨ ∼ G) ⊃ R] & C c. ∼ (G ∨ C) 6. Which of the following are sentences (well-formed formulas) of SL? For those that are not, state why not. a. B ⊃ (K ∼ ∨ D) b. (D
( J ⊃ B))
J) c. ∼ J
∼ ( J ∨ ∼ K) d. (W ∨ ∼ W) ⊃ ∼ W ∨ W ANSWERS 1. a. Both either it is not the case that I will go to Boston or it rains and (Bill will go to Boston if and only if Bill’s car is running). (∼ W ∨ R) & (B
C) b. Both both mares eat oats and bears eat oats and little lambs eat ivy. (M & B) & L c. Not a truth-functional compound. It is its own paraphrase and can be symbolized as ‘W’. d. Both Michael Crichton is one of the most creative people alive and if Michael Crichton tries his hand at television, then Michael Crichton will be a success. C & (T ⊃ S) e. It is not the case that two heads are better than one. ∼ T 2. Either the local bookstore carries novels by Mishima or it is not the case that I will be able to complete my bibliography. Both it is not the case that some of Mishima’s novels are in the library and if it is not the case that some of Mishima’s novels are in the library then it is not the case that the local bookstore carries novels by Mishima. INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK 15 If it is not the case that I will be able to complete my bibliography then it is not the case that either I can go home this weekend or I can go home next weekend. It is not the case that I can go home next weekend. B ∨ ∼ C ∼ S & (∼ S ⊃ ∼ B) ∼ C ⊃ ∼ (H ∨ N) ∼ N 3. P ∼P P Q P& Q P∨Q P⊃Q P
Q T F T T T T T T F T T F F T F F F T F T T F F F F F T T 4. a. F b. F c. T d. F e. F 5. a. The odds on Cinch Bet are good if and only if Bright Horse is the favorite, but the odds on him aren’t good. b. If Bright Horse isn’t the favorite or the odds on him aren’t good, then the track is muddy; and the odds on Cinch Bet are good. c. Neither the odds on Bright Horse nor the odds on Cinch Bet are good. 6. a. Not a sentence: ‘∼’ cannot immediately precede a binary connective b. Not a sentence: too many right parentheses c. Sentence d. Not a sentence: too few parentheses LOGIC TEST 2 1. Give a truth-functional paraphrase of each of the following. Symbolize each paraphrase in SL, being sure to indicate which sentences your sentence letters abbreviate. a. The track is muddy, and, although Bright Horse is favored to win, I’ll bet he won’t. b. We’ll have a flood in the basement if that pipe doesn’t stop leaking. c. Jazz is better than rock, but neither beats country music! d. This novel will sell if and only if the author gets the right publisher. e. Miracles probably never happen. 2. Give a truth-functional paraphrase of the following argument and put it into standard form. Symbolize the paraphrased argument in SL, indicating which sentences your sentence letters abbreviate. You may have another drink only if Jeff or Stanley can drive you home. Neither Herbert nor Jeff is sober. If either Jeff or Stanley is not sober, then neither is sober. Furthermore, if neither is sober, neither can drive you home. Hence you may not have another drink. 3. Give the characteristic truth-tables for the following connectives: P ∼P P Q P& Q P∨Q P⊃Q P
Q T T T F T F F T F F 4. Assuming that ‘A’ has the truth-value T and ‘B’ has the truth-value F, what is the truth-value of each of the following sentences? a. ∼ A b. B ∨ A c. B ⊃ A d. A
B e. B & B 5. Use the following abbreviations to give clear, idiomatic English readings for a–c. G: Granola is a healthy food. H: Perky Dog Chow is a healthy food. C: Granola looks appetizing. D: Perky Dog Chow looks appetizing. a. ∼ C & ∼ (D ∨ H) b. C
(∼ G ∨ ∼ H) c. G ⊃ C 6. Which of the following are sentences (well-formed formulas) of SL? For those that are not, state why not. a. A
(C ∨ C) ∨ D b. B ⊃ (A
∼ B) c. ∼ ∼ A d. A(& B & A) e. (A ⊃ B) & ∼ (A ⊃ B) 16 INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK INSTRUCTOR’S MANUAL/TEST BANK FOR THE LOGIC BOOK 17 ANSWERS 1. a. Both the track is muddy and both Bright Horse is favored to win and I’ll bet Bright Horse will not win. T & (B & I) b. If it is not the case that that pipe does stop leaking then we’ll have a flood in the basement. ∼ P ⊃ F c. Both jazz is better than rock and it is not the case that either jazz beats country music or rock beats country music. B & ∼ ( J ∨ R) d. This nove