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

1. No vampire movies are films without blood.2. All governments that bargain with terrorists are governments that encourage terrorism.3. Some symphony orchestras are organizations on the brink of bankruptcy.4. Some Chinese leaders are not thoroughgoing opponents of capitalist economics.5. All human
Change the quality but not the quantity of the following categorical propositions:1. All drunk drivers are threats to others on the highway.2. No wildlife refuges are locations suitable for condominium developments.3. Some slumlords are people who eventually wind up in jail.4. Some CIA operatives
Change the quantity but not the quality of the following categorical propositions:1. All owners of pit bull terriers are people who can expect expensive lawsuits.2. No tax proposals that favor the rich are fair proposals.3. Some gradeschool administrators are people who choke the educational
Change both the quality and the quantity of the following categorical propositions:1. All oil spills are events catastrophic to the environment.2. No alcoholics are people with a healthy diet.3. Some Mexican vacations are episodes that end with gastrointestinal distress.4. Some corporate lawyers
1. No life decisions are happenings based solely on logic.2. All electric motors are machines that depend on magnetism.3. Some political campaigns are mere attempts to discredit opponents.4. Some rockmusic lovers are not fans of JayZ.5. All redistricting plans are sources of controversy.6. No tax
1. No sculptures by Rodin are boring creations. Therefore, all sculptures by Rodin are boring creations.2. It is false that some lunar craters are volcanic formations. Therefore, no lunar craters are volcanic formations.3. All trial lawyers are people with stressful jobs. Therefore, some trial
1. All neutron stars are things that produce intense gravity. All neutron stars are extremely dense objects. Therefore, all extremely dense objects are things that produce intense gravity.2. No insects that eat mosquitoes are insects that should be killed. All dragonflies are insects that eat
1. Some nebulas are clouds of gas.Some clouds of gas are objects invisible to the naked eye.Therefore, some objects invisible to the naked eye are nebulas.2. No individuals sensitive to the difference between right and wrong are people who measure talent and success in terms of wealth.All
Answer "true" or "false" to the following statements: 1. If a standard-form categorical syllogism violates one of the first four rules, it may still be valid. 2. If a valid standard-form syllogism has an E statement as its conclusion, then both the major and minor terms must be distributed in the
1. Some intelligible statements are true statements, because all unintelligible statements are meaningless statements and some false statements are meaningful statements.2. Some people who do not regret their crimes are convicted murderers, so some convicted murderers are people insusceptible of
1. No objects that sink in water are chunks of ice, and no objects that float in water are things at least as dense as water. Accordingly, all chunks of ice are things less dense than water.2. Some proposed flights to Mars are inexpensive ventures, because all unmanned space missions are
1. Physicists are the only scientists who theorize about the nature of time, and Stephen Hawking certainly does that. Therefore, Stephen Hawking must be a physicist.2. Whenever suicide rates decline, we can infer that people's lives are better adjusted. Accordingly, since suicide rates have been
1. Wherever icebergs are present, threats to shipping exist. Icebergs are not present in the South Pacific. Hence, there are no threats to shipping in the South Pacific.2. According to surveys, there are college students who think that Africa is in North America. But anyone who thinks that has no
1. Any city that has excellent art museums is a tourist destination. Therefore, Paris is a tourist destination, because it has excellent art museums.2. Miranda Lambert sings what she wants. Hence, since Miranda sings country songs, it follows that she must want to sing country songs.3. Not all
1. Some police chiefs undermine the evenhanded enforcement of the law, because anyone who fixes parking tickets does that.2. Any form of cheating deserves to be punished, and plagiarism is a form of cheating.3. Carrie Underwood is a talented singer. After all, she’s won several Grammy
Translate the enthymemes in Part I of this exercise into standard-form categorical syllogisms and test them for validity.1. Some police chiefs undermine the evenhanded enforcement of the law, because anyone who fixes parking tickets does that.2. Any form of cheating deserves to be punished, and
1. No Republicans are Democrats, so no Republicans are big spenders, since all big spenders are Democrats.2. Some latchkey children are not kids who can stay out of trouble, for some youngsters prone to boredom are latchkey children, and no kids who can stay out of trouble are youngsters prone to
1. If the Defense Department is so intent on fighting alcohol abuse, why does it make alcohol so readily available and acceptable? Alcohol is tax free at post liquor stores, and enlisted men's and officers' clubs make drinking almost a mandatory facet of military life.2. All aid to Israel should be
1. The Constitution bans any law that is so vague that "men of common intelligence must necessarily guess at its meaning." Sexual harassment laws, however, are so vague that no one knows what they mean. 2. College students of today are the higher-income taxpayers of tomorrow. Congress should
Translate the arguments in the following dialogue into standard-form categorical syllogisms. The dialogue contains more than twenty arguments, and most are expressed in the form of enthymemes. The first translated syllogism may be found in the answer section.Do Kids Make Parents Happy?Tad and Lara,
Rewrite the following sorites in standard form, reducing the number of terms when necessary. Then supply the intermediate conclusions and test with Venn diagrams.1. No B are C.Some D are C.All A are B.Some D are not A.2. No C are D.All A are B.Some C are not B.Some D are not A.3. No S are M.All F
For the sorites in Part I above, rewrite each in standard form, reducing the number of terms when necessary. Then use the five rules for sorites to test each for validity.1. No B are C.Some D are C.All A are B.Some D are not A.2. No C are D.All A are B.Some C are not B.Some D are not A.3. No S are
1. Whatever produces oxygen supports human life.Rain forests produce oxygen.Nothing that supports human life should be destroyed.Rain forests should not be destroyed.2. No restrictive trade policies fail to invite retaliation.Trade wars threaten our standard of living.Some Chinese trade policies
1. No ducks waltz.No officers ever decline to waltz.All my poultry are ducks.My poultry are not officers.2. No experienced person is incompetent.Jenkins is always blundering.No competent person is always blundering.Jenkins is inexperienced.3. No terriers wander among the signs of the zodiac.Nothing
Reconstruct the syllogistic forms from the following combinations of mood and figure:1. OAE-32. EIA-43. AII-34. IAE-15. AOO-26. EAO-47. AAA-18. EAO-29. OEI-310. OEA-4
Construct the following syllogisms.1. An EIO-2 syllogism with these terms-major-dogmatists; minor- theologians; middle-scholars who encourage freethinking.2. An unconditionally valid syllogism in the first figure with a particular affirmative conclusion and these terms: major-people incapable of
Answer "true" or "false" to the following statements: 1. Every syllogism is a categorical syllogism. 2. Some categorical syllogisms cannot be put into standard form. 3. The statements in a categorical syllogism need not be expressed in standard form. 4. The statements in a standard-form categorical
1. All corporations that overcharge their customers are unethical businesses.Some unethical businesses are investor-owned utilities.Therefore, some investor-owned utilities are corporations that overcharge their customers.2. No fossil fuels are renewable forms of energy.Some combustible gases are
1. All circular triangles are plane figures. All circular triangles are three-sided figures. Therefore, some three-sided figures are plane figures. 2. All supernovas are objects that emit massive amounts of energy. All quasars are objects that emit massive amounts of energy. Therefore, all quasars
1. All currently living dinosaurs are giant reptiles. All giant reptiles are ectothermic animals. Therefore, some ectothermic animals are currently living dinosaurs. 2. All survivalists are people who enjoy simulated war games. No people who enjoy simulated war games are soldiers who have tasted
1. All impulse buyers are consumers with credit cards.All shopaholics are impulse buyers.Therefore, all shopaholics are consumers with credit cards.2. No pediatricians are individuals who jeopardize the health of children.All faith healers are individuals who jeopardize the health of
1. No P are M.All S are M.2. Some P are not M.Some M are S.3. Some M are P.All S are M.4. Some M are not P.All M are S.5. Some P are M.All M are S.Use Venn diagrams to obtain the conclusion that is validly implied by each of the above sets of premises. If no conclusion can be validly drawn, write
1. No P are M.All S are M.2. Some P are not M.Some M are S.3. Some M are P.All S are M.4. Some M are not P.All M are S.5. Some P are M.All M are S.Use Venn diagrams to obtain the conclusion that is validly implied by each of the following sets of premises. If no conclusion can be validly drawn,
1. No M are P.Some S are not M.2. All M are P.All S are M.3. All P are M.All S are M.4. No P are M.Some M are S.5. No P are M.No M are S.Use Venn diagrams to obtain the conclusion that is validly implied by each of the following sets of premises. If no conclusion can be validly drawn, write "no
Answer "true" or "false" to the following statements: 1. In the use of Venn diagrams to test the validity of syllogisms, marks are sometimes entered in the diagram for the conclusion. 2. When an X is placed on the arc of a circle, it means that the X could be in either (or both) of the two areas
Reconstruct the following syllogistic forms and use the five rules for syllogisms to determine if they are valid from the Boolean standpoint, conditionally valid from the Aristotelian standpoint, or invalid. For those that are conditionally valid, identify the condition that must be fulfilled. For
1. Cartier does not make cheap watches. 2. Arizona has a national park but Nebraska does not. 3. Either Stanford or Tulane has an architecture school. 4. Both Harvard and Baylor have medical schools. 5. If Chanel has a rosewood fragrance, then so does Lanvin. 6. Chanel has a rosewood fragrance if
1. Renowned economist Harold Carlson makes the following prediction: "The balance of payments will decrease if and only if interest rates remain steady; however, it is not the case that either interest rates will not remain steady or the balance of payments will decrease." What can we say about
1. If national elections deteriorate into TV popularity contests, then smooth-talking morons will get elected. Therefore, if national elections do not deteriorate into TV popularity contests, then smooth-talking morons will not get elected. (N, S)2. Brazil has a huge foreign debt. Therefore, either
Determine whether the following symbolized arguments are valid or invalid by constructing a truth table for each.1. K ⊃ ∼ K / ∼K2. R ⊃ R / R3. P ≡ ∼ N / N ∨ P4. ∼(G ∙ M)M ∨ G / G5. K ≡ L∼(L
When possible, compute the truth values of the simple components in the following compound propositions. If no truth value can be computed, write a question mark (?) under the letter or letters with unknown truth value.1. K ∨ DF T2. Q ⊃ NT3. B ≡ DT F4. N ⊃ GT
Use indirect truth tables to determine whether the following arguments are valid or invalid.1. B ⊃ C∼ C∼B2. ∼E ∨ F∼E∼F3. P ⊃ (Q ∙ R)R ⊃ SP ⊃ S4. ∼ (I ≡ I)/∼ (I ⊃ I)5.6.7.8.9.10.11.12.13.14.15.
Use indirect truth tables to determine whether the following groups of statements are consistent or inconsistent.1. . K ≡ (R ∨ M)K ∙ ∼ RM ⊃ ∼ K2.3.4.5. P ∨ ∼ SS ∨ ∼ TT ∨ ∼ XX ∨ ∼ JJ
Interpret the following symbolized arguments in light of the eight argument forms presented in this section. In some cases a symbolized argument must be rewritten using commutativity or double negation before it becomes an instance of one of these forms. Those not having a named form are
1. A Boeing 757 crashed into the Pentagon on 9/11 only if two giant engines were found outside the building. It is not the case that two giant engines were found outside the building. Therefore, a Boeing 757 did not crash into the Pentagon on 9/11. (B, G)2. If Michelangelo painted the ceiling of
If Melinda spends the night studying, she will miss the party; but if she does not spend the night studying, she will fail the test tomorrow. Melinda must either spend the night studying or not studying. Therefore, she will either miss the party or fail the test. (S, M, F)Identify the following
If we prosecute suspected terrorists, then we risk retaliation by other terrorists; but if we release them, then we encourage terrorism. Since we must either prosecute or release suspected terrorists, we either risk retaliation by other terrorists or we encourage terrorism. (P, R, T, E) Identify
If we build our home in the valley, it will be struck by floods; and if we build it on the hilltop, it will be hit by lightning. Since we must either build it in the valley or on the hilltop, our home will either be struck by floods or hit by lightning. (V, F, H, L) Identify the following dilemmas
If psychotherapists respect their clients' right to confidentiality, then they will not report child abusers to the authorities; but if they have any concern for the welfare of children, then they will report them. Psychotherapists must either report or not report child abusers to the authorities.
If corporations are to remain competitive, then they must not spend money to neutralize their toxic waste; but if the environment is to be preserved, then corporations must spend money to neutralize their toxic waste. Corporations either will or will not spend money to neutralize their toxic waste.
If physicians pull the plug on terminally ill patients, then they risk being charged with murder; but if they do not pull the plug, they prolong their patients' pain and suffering. Since physicians with terminally ill patients must do one or the other, either they risk being charged with murder or
If the Mitchells get a divorce, they will live separately in poverty; but if they stay married, they will live together in misery. Since they must either get a divorce or stay married, they will either live separately in poverty or together in misery. (D, S, M, T) Identify the following dilemmas as
If college students want courses that are interesting and rewarding, then they must major in liberal arts; but if they want a job when they graduate, then they must major in business. College students will either not major in liberal arts, or they will not major in business. Therefore, either they
If merchants arrest suspected shoplifters, then they risk false imprisonment; but if they do not arrest them, they risk loss of merchandise. Merchants must either arrest or not arrest suspected shoplifters. Therefore, they will either risk false imprisonment or loss of merchandise. (A, F,
If women threatened with rape want to avoid being maimed or killed, then they must not resist their assaulter; but if they want to ensure successful prosecution of the assailant, they must resist him. Since women threatened with rape must do one or the other, either they will risk being maimed or
1. Unless we reduce the incidence of child abuse, future crime rates will increase. (R, F) 2. If pharmaceutical makers conceal test results, they are subject to substantial fines. (P, S) 3. African safaris are amazing, but they are also expensive. (A, E) 4. Cigarette manufacturers are neither
1. There is a simple way to put a big dent in the national human-organ shortage: Allocate organs first to the people who have agreed to donate their own. Giving organs first to registered donors would persuade more people to register, and that would make the allocation system fairer. People who
Determine which of the following are not well-formed formulas.1. (S ∙ ∼T) ∨ (U ∙ W)2. ∼(K ∨ L) ∙ (⊃ G ∨ H)3. (E ≡ F) ∨ (W ≡ X)4. (B ⊃ T) ≡ (C ⊃ U )5. (F ≡ Q) ∙
Identify the main operator in the following propositions.1. ∼(A ∨ M ) ∙ ∼ (C ⊃ E )2. (G ∙ ∼ P) ⊃ (H ∨ ∼ W)3. ∼[P ∙ (S ≡ K)]4. ∼(K ∙ ∼O) ≡ ∼(R ∨ ∼B)5. (M
1. It is not the case that Hitler ran the Third Reich.2. Nixon resigned the presidency and Lincoln wrote the Gettysburg Address.3. France bombed Pearl Harbor, or Lindbergh crossed the Atlantic.4. Hitler ran the Third Reich and Nixon did not resign the presidency.5. Edison invented the telephone, or
Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.1. A ∙ X2. B ∙ ∼ Y3. X ∨ ∼Y4. ∼C ∨ Z5. B ⊃ ∼Z6.
When possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth values. If the truth value of the statement cannot be determined, write "undetermined."1. A ∨ P2. Q ∨ Z3. Q ∙ Y4. Q ∙ A5.
Use truth tables to determine whether the following symbolized statements are tautologous, self-contradictory, or contingent.1. N ⊃ (N ⊃ N)2. (G ⊃ G) ⊃ G3. (S ⊃ R) ∙ (S ∙ ∼ R)4.
Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or inconsistent. First, determine whether the pairs of propositions are logically equivalent or contradictory; then, if these relations do not apply, determine if
For each of the following lists of premises, derive the conclusion and supply the justification for it. There is only one possible answer for each problem.(1) 1. G ⊃ F2. ∼ F3. _______ ____(2) 1. S2. S ⊃ M3. _______ ____(3) 1. R ⊃ D2. E ⊃ R3.
In the following symbolized arguments, derive the line needed to obtain the conclusion (last line), and supply the justification for both lines.1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.
Use the first thirteen rules of inference to derive the conclusions of the following symbolized arguments:1.2.3.4.5.6.7.8.9.10.
1. Either health-care costs are skyrocketing and they are attributable to greedy doctors, or health-care costs are skyrocketing and they are attributable to greedy hospitals. If health-care costs are skyrocketing, then both the government should intercede and health care may have to be rationed.
For each of the following lists of premises, derive the indicated conclusion and complete the justification. For tautology, derive a conclusion that is simpler than the premise.1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.
In the following symbolized arguments, derive the line needed to obtain the conclusion (last line), and supply the justification for both lines.1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.
Use the eighteen rules of inference to derive the conclusions of the following symbolized arguments.1.2.3.4.5.6.7.8.9.10.
1. If sports-shoe manufacturers decline to use kangaroo hides in their products, then Australian hunters will cease killing millions of kangaroos yearly. It is not the case that both Australian hunters will cease killing millions of kangaroos yearly and the kangaroo will not be saved from
Use conditional proof and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using conditional proof.1.2.3.4.5.6.7.8.9.10.
1. If high-tech products are exported to Russia, then domestic industries will benefit. If the Russians can effectively utilize high-tech products, then their standard of living will improve. Therefore, if high-tech products are exported to Russia and the Russians can effectively utilize them, then
The following symbolized arguments are missing a premise. Write the premise needed to derive the conclusion (last line), and supply the justification for the conclusion. Try to construct the simplest premise needed to derive the conclusion.1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.
Use either indirect proof or conditional proof (or both) and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using indirect proof or conditional proof.1.2.3.4.5.6.7.8.9.10.
1. If government deficits continue at their present rate and a recession sets in, then interest on the national debt will become unbearable and the government will default on its loans. If a recession sets in, then the government will not default on its loans. Therefore, either government deficits
Use conditional proof or indirect proof and the eighteen rules of inference to establish the truth of the following tautologies.1. P ⊃ [(P ⊃ Q) ⊃ Q]2. (∼P ⊃ Q) ∨ (P ⊃ R)3. P ≡ [P ∨ (Q ⊃ P)]4. (P ⊃
Use the first four rules of inference to derive the conclusions of the following symbolized arguments.1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.
1. If OxyContin is addictive, then either the pharmaceutical industry has stopped making it or thousands of patients are becoming addicted to it. The pharmaceutical industry has not stopped making OxyContin. Also, OxyContin is addictive. Therefore, thousands of patients are becoming addicted to it.
For each of the following lists of premises, derive the indicated conclusion and complete the justification. In problems 4 and 8 you can add any statement you choose.(1) 1. S ∨ H2. B ⊃ E3. R ⊃ G4. _____ ____, Simp(2) 1. (N ⊃ T) ∙ (F ⊃ Q)2.
In the following symbolized arguments, derive the line needed to obtain the conclusion (last line), and supply the justification for both lines.1.2.3.4.5.6.7.8.9.10.
Use the first eight rules of inference to derive the conclusions of the following symbolized arguments:1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30.
1. If topaz is harder than quartz, then it will scratch quartz and also feldspar. Topaz is harder than quartz and it is also harder than calcite. Therefore, either topaz will scratch quartz or it will scratch corundum. (T, Q, F, C, O)2. If clear-cutting continues in primary forests and the
For each of the following lists of premises, derive the indicated conclusion and complete the justification. For double negation, avoid the occurrence of triple tildes. Exercise 6 has two possible answers.1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.
1. Elaine is a chemist. (C)2. Nancy is not a sales clerk. (S)3. Neither Wordsworth nor Shelley was Irish. (I)4. Rachel is either a journalist or a newscaster. (J, N)5. Intel designs a faster chip only if Micron does. (D)6. Belgium and France subsidize the arts only if Austria or Germany expand
Use either indirect proof or conditional proof to derive the conclusions of the following symbolized arguments.1.2.3.4.5.6.7.8.9.10.
1. All ambassadors are wealthy. Furthermore, all Republicans are clever. Therefore, all Republican ambassadors are clever and wealthy. (A, W, R, C)2. All senators are well liked. Also, if there are any well-liked senators, then O'Brien is a voter. Therefore, if there are any senators, then O'Brien
Use the counterexample method to prove that the following symbolized arguments are invalid.1.2. 3. 4. 5. 6. 7. 8. 9. 10.
Use the finite universe method to prove that the following symbolized arguments are invalid.1.2.3.4.5.
1. Violinists who play well are accomplished musicians. There are some violinists in the orchestra. Therefore, some musicians are accomplished. (V, P, A, M, O)2. Pianists and harpsichordists are meticulous. Alfred Brendel is a pianist. Therefore, everyone is meticulous. (P, H, M)3. If there are any
1. Charmaine read Paradise Lost. (Rxy: x read y)2. Whoever reads Paradise Lost is educated. (Rxy: x reads y; Ex: x is educated)3. James is a friend of either Ellen or Connie. (Fxy: x is a friend of y)4. If James has any friends, then Marlene is one of them. (Fxy: x is a friend of y)5. Dr. Jordan
Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1.2.3.4.5.6.7.8.9.10.
1. Any professional can outplay any amateur. Jones is a professional but he cannot outplay Meyers. Therefore, Meyers is not an amateur. (Px: x is a professional; Ax: x is an amateur; Oxy: x can outplay y)2. Whoever is a friend of either Michael or Paul will receive a gift. If Michael has any
1. Dr. Seuss is Theodore Geisel. (s, g)2. Auguste Renoir is not Claude Monet. (r, m)3. Marilyn Monroe is Norma Jean Baker. (m, b)4. Hermann Hesse is not André Gide. (h, g) Statements involving "only," "the only," and "no . . . except"5. Only Linus Pauling has won two unshared Nobel prizes. (Wx: x
Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1.2.3.4.5.
1. Some of Jane Collier's novels are interesting. The only novel Jane Collier wrote is The Cry. Therefore, The Cry is interesting. (Nx: x is a novel; Wxy: x wrote y; Ix: x is interesting; j: Jane Collier; c: The Cry)2. Ronald Reagan was the oldest U.S. president. Woodrow Wilson was a U.S.
Use the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Do not use either conditional proof or indirect proof.1.2.3.4.5.6.7.8.9.10.
1. Oranges are sweet. Also, oranges are fragrant. Therefore, oranges are sweet and fragrant. (O, S, F)2. Tomatoes are vegetables. Therefore, the tomatoes in the garden are vegetables. (T, V, G)3. Apples and pears grow on trees. Therefore, apples grow on trees. (A, P, G)4. Carrots are vegetables and
Use the quantifier negation rule together with the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Do not use either conditional proof or indirect proof.1.2.3.4.5.

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