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logic functions and equations
A Concise Introduction To Logic 11th Edition Patrick J. Hurley - Solutions
11. For each of the following lists of premises, derive the conclusion and supply the justifi cation for it. Th ere is only one possible answer for each problem. *(1) 1. G>F 2.-F 3. (2) 1. S 2. S>M 3. (3) 1. R-D 2. E-R 3. (4) 1. Bv C 2.-B 3. (5) 1. N 2. Nv F 3. N-K 4.
★10. More than a million adult videocassettes are rented each week. Nor, as the propagandists would have you believe, does viewing such material lead to violent sex crimes. If it did, there would be over one million such crimes per week. Th e following selections were taken from letters to the
9. Regarding the bill to require parental consent for a minor’s abortion, I would like to point out that the pious platitudes about parental authority quickly fall by the wayside when the minor wants to keep the baby and the parents say, “Don’t be silly! You have an abortion and fi nish your
8. If the death penalty deters one person from becoming a murderer, it is eff ective.Th ere are also some other important reasons for having the death penalty.First, the families and friends of innocent victims have the right to see eff ective retribution. Second, terminating the life of a killer
★7. We cannot aff ord to close the library at Central Juvenile Hall. Th ese young people in particular need to have access to ideas, dreams, and alternative ways of living. It can make the difference for many students who might become interested in reading for the fi rst time in their lives while
6. A country that replaces the diseased hearts of old white men but refuses to feed schoolchildren, pay women adequately, educate adolescents, or care for the elderly—that country is doomed. We are acting as if there is no tomorrow.Where is our shame?(Robert Birch) Th e following selections were
5. If voluntary school prayer for our children is going to make them more moral, then just think what mandatory church attendance on Sunday could do for the rest of us.(Roderick M. Boyes) Th e following selections were taken from letters to the editor of newspapers. Each contains one or more
★4. Most educators believe math instructors ought to emphasize group problem solving. If group problem solving is so important (and I think it is), why do we place such emphasis on individual testing? Th e national math test is a mistake.(Frederick C. Thayer) Th e following selections were taken
3. The religious right, in its impassioned fervor to correct our alleged moral wrongs and protect the rights of our unborn “children,” may one day realize its ultimate goal of a constitutional amendment banning abortion. And what will the punishment be for those caught performing or receiving
2. OK, I’ve tried it for a week again this year, but I still don’t like daylight- saving time. My grass is brown enough already—it doesn’t need another hour of daylight each day. Let’s turn the clocks back to the way God intended—standard time.(Jim Orr) Th e following selections were
★1. Th ere is a simple way to put a big dent in the national human organ shortage:allocate organs fi rst to the people who have agreed to donate their own. Giving organs fi rst to registered donors would persuade more people to register, and that would make the allocation system fairer. People
★10. 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. Identify the
9. 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
8. If merchants arrest suspected shoplift ers, 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 shoplift ers. Th erefore, they will either risk false imprisonment or loss of merchandise. Identify
★7. 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. Th erefore,
6. 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. Identify the following dilemmas as either
5. 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 suff ering. Since physicians with terminally ill patients must do one or the other, either they risk being charged with
★4. 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
3. If psychotherapists respect their clients’ right to confi dentiality, 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
2. If we build our home in the valley, it will be struck by fl oods; 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 fl oods or hit by lightning. Identify the following dilemmas as
★1. 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. Identify the following
20. If tax credits are given for private education, then the government will be supporting religion; but if tax credits are not given for private education, then some parents will end up paying double tuition. Either tax credits will or will not be given for private education. Th erefore, either
★19. If sea levels rise twenty feet worldwide, then coastal cities from New York to Sydney will be inundated. If the ice sheets on Antarctica slip into the sea, then sea levels will rise twenty feet worldwide. Th erefore, if the ice sheets on Antarctica slip into the sea, then coastal cities from
18. If coal burning continues, then heavy metals will be released into the atmosphere.If heavy metals are not released into the atmosphere, then nervous system damage will decrease. Th erefore, if coal burning does not continue, then nervous system damage will decrease. Translate the following
17. Either the dinosaurs were not cold-blooded or they were not the ancestors of modern birds. Th e dinosaurs were the ancestors of modern birds. Th erefore, the dinosaurs were not cold-blooded. Translate the following arguments into symbolic notation and then interpret them in light of the eight
★16. If Mexico does not get its population growth under control, then its unemployment problem will never be solved. Mexico’s unemployment problem will never be solved. Therefore, Mexico will not get its population growth under control. Translate the following arguments into symbolic notation
15. Insurance companies contribute millions of dollars to political campaigns.But if that is so, then meaningful insurance reform is impossible. Th erefore, meaningful insurance reform is impossible. Translate the following arguments into symbolic notation and then interpret them in light of the
14. Either industrial pollutants will be more stringently controlled, or acid rain will continue to fall. Industrial pollutants will be more stringently controlled.Th erefore, acid rain will not continue to fall. Translate the following arguments into symbolic notation and then interpret them in
★13. If we want to arrest criminals, then police must engage in high-speed chases;but if we want to protect motorists, then police must not engage in high-speed chases. Since police must either engage or not engage in high-speed chases, either we will not arrest criminals or not protect
12. If life is always better than death, then people do not commit suicide. People do commit suicide. Th erefore, life is not always better than death. Translate the following arguments into symbolic notation and then interpret them in light of the eight argument forms presented in this section. In
11. If Prohibition succeeded in the 1920s, then the war on drugs will succeed today. But Prohibition did not succeed in the 1920s. Th erefore, the war on drugs will not succeed today. Translate the following arguments into symbolic notation and then interpret them in light of the eight argument
★10. If limits are imposed on medical malpractice suits, then patients will not be adequately compensated for their injuries; but if the cost of malpractice insurance continues to rise, then physicians will be forced out of business. Limits will not be imposed, and the cost of malpractice
9. If high school clinics are to stem the tide of teenage pregnancy, then they must dispense birth control devices; but if they want to discourage illicit sex, then they must not dispense these devices. Since high school clinics must either dispense or not dispense birth control devices, either
8. If TV viewing provides genuine relaxation, then TV enhances the quality of life. But TV viewing does not provide genuine relaxation. Th erefore, TV does not enhance the quality of life. Translate the following arguments into symbolic notation and then interpret them in light of the eight
★7. Nano-thermite is present in the debris from the World Trade Center. But if that is so, then the buildings were brought down by controlled demolition.Th erefore, the buildings were brought down by controlled demolition. Translate the following arguments into symbolic notation and then
6. If the sun is a variable star, then its energy will drop drastically at some point in the future. If the sun’s energy drops drastically at some point in the future, then the earth will become a giant ice-ball. Th erefore, if the sun is a variable star, then the earth will become a giant
5. Either drivers are forbidden to send text messages, or the highways will not become safer. Drivers are forbidden to send text messages. Therefore, the highways will become safer. Translate the following arguments into symbolic notation and then interpret them in light of the eight argument forms
★4. Either the wealthiest people are the happiest, or it is not the case that money can buy everything. Th e wealthiest people are not the happiest. Th erefore, money cannot buy everything. Translate the following arguments into symbolic notation and then interpret them in light of the eight
3. If you enter the teaching profession, you will have no money for vacations;and if you do not enter the teaching profession, you will have no time for vacations. Since you must either enter or not enter the teaching profession, it follows that either you will have no money or no time for
2. If Michelangelo painted the ceiling of the Sistine Chapel, then he was familiar with stories from the Old Testament. Michelangelo was familiar with stories from the Old Testament. Th erefore, Michelangelo painted the ceiling of the Sistine Chapel. Translate the following arguments into symbolic
★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. Th erefore, a Boeing 757 did not crash into the Pentagon on 9/11. Translate the following arguments into
11. 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. Th ose not having a named form are
11. 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. Th ose not having a named form are
11. 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. Th ose not having a named form are
11. 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. Th ose not having a named form are
11. 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. Th ose not having a named form are
11. 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. Th ose not having a named form are
10. A ∨ Z A ⊃ (T • F)Z ⊃ (M • Q)Q ⊃ ∼F T ⊃ ∼M M ⊃ A Use indirect truth tables to determine whether the following groups of statements are consistent or inconsistent.
9. G ⊃ P P ⊃ (A • ∼G)(R ∨ T) ⊃ G Y ⊃ R B ⊃ T Y ∨ B Use indirect truth tables to determine whether the following groups of statements are consistent or inconsistent.
8. (E ∨ H) ⊃ (K • D)D ⊃ (M • B)B ⊃ ∼E∼(H ∨ K)D ⊃ B Use indirect truth tables to determine whether the following groups of statements are consistent or inconsistent.
★7. S ⊃ (R ≡ A)A ⊃ (W • ∼R)R ≡ (W ∨ T)S • U U ⊃ T Use indirect truth tables to determine whether the following groups of statements are consistent or inconsistent.
6. (Q ∨ K) ⊃ C(C • F) ⊃ (N ∨ L)C ⊃ (F • ∼L)Q • ∼N Use indirect truth tables to determine whether the following groups of statements are consistent or inconsistent.
5. P ∨ ∼S S ∨ ∼T T ∨ ∼X X ∨ ∼J J ∨ ∼P Use indirect truth tables to determine whether the following groups of statements are consistent or inconsistent.
★4. (N ∨ C) ≡ E N ⊃ ∼(C ∨ H)H ⊃ E C ⊃ H Use indirect truth tables to determine whether the following groups of statements are consistent or inconsistent.
3. (G ∨ ∼Q) ⊃ (F ∨ B)∼(F ∨ Q)B ⊃ N(F ∨ N) ⊃ Q Use indirect truth tables to determine whether the following groups of statements are consistent or inconsistent.
2. F ≡ (A • ∼P)A ⊃ (P • S)S ⊃ ∼F A • ∼F Use indirect truth tables to determine whether the following groups of statements are consistent or inconsistent.
★1. K ≡ (R ∨ M)K • ∼R M ⊃ ∼K Use indirect truth tables to determine whether the following groups of statements are consistent or inconsistent.
13. Use indirect truth tables to determine whether the following arguments are valid or invalid. 14. G(HI) H K>(L.M) KvJ L.G 15. Nv-O PVO P>Q (NvQ)>(R.S) S>(ROT) 0>(TU) U
13. Use indirect truth tables to determine whether the following arguments are valid or invalid. 11. (AB) (CD) (-AV-B) E (-CV-D)>E 12. F G ~HvI (GVI)>J (Fv H) *13. (Av B)>(C. D) (XV-Y)(-C-W) (XVZ)>(AE) -X
13. Use indirect truth tables to determine whether the following arguments are valid or invalid. *7. G H H-1 >G 1 I 8. J>(~L~K) K (LM) (LVM) N JON 9. P.(QVR) (P+R)-(SVT) (-Sv-T)~(PQ) S=T 10. (MvN)0 0> (NvP) M>(-QON) (QM)>-P N=0
13. Use indirect truth tables to determine whether the following arguments are valid or invalid. 5. W> (XY) X>(YZ) W>(X> Z) 6. A> (BVC) C>(D.E) -B AS-E
13. Use indirect truth tables to determine whether the following arguments are valid or invalid. 3. P(QR) R-S P>S *4. ~(I=)) -(1-1)
13. Use indirect truth tables to determine whether the following arguments are valid or invalid. 1. BC -C -B 2. -EvF -E -F
12. 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. KvD FT 2. QN T 3. B=D TF *4. N-G TT 5. S B TF 6. K.B T *7. CV A TF 8.
11. Determine whether the following symbolized arguments are valid or invalid by constructing a truth table for each. *1. K>~K -K 2. R-R R 3. P=~N NvP *4. ~(G.M) MV-G -G 5. K=-L ~L~K) K-L 6. Z E>(ZE) *7. (W.-X) ~(X-W) Xv W 8. C=D 11. (K=S) S (RVK) RV-S 12. E(F.G) F>(GH) E-H *13. A> (NVQ) ~(NV-A) A
★10. If racial quotas are adopted for promoting employees, then qualifi ed employees will be passed over; but if racial quotas are not adopted, then prior discrimination will go unaddressed. Either racial quotas will or will not be adopted for promoting employees. Th erefore, either qualifi ed
9. Either the USS Arizona or the USS Missouri was not sunk in the attack on Pearl Harbor. Th erefore, it is not the case that either the USS Arizona or the USS Missouri was sunk in the attack on Pearl Harbor. Translate the following arguments into symbolic form. Th en determine whether each is
8. If microchips are made from diamond wafers, then computers will generate less heat. Computers will not generate less heat and microchips will be made from diamond wafers. Th erefore, synthetic diamonds will be used for jewelry. Translate the following arguments into symbolic form. Th en
★7. Einstein won the Nobel Prize either for explaining the photoelectric eff ect or for the special theory of relativity. But he did win the Nobel Prize for explaining the photoelectric eff ect. Th erefore, Einstein did not win the Nobel Prize for the special theory of relativity. Translate the
6. Th e disparity between rich and poor is increasing. Th erefore, political control over economic equality will be achieved only if restructuring the economic system along socialist lines implies that political control over economic equality will be achieved. Translate the following arguments into
5. If high school graduates are defi cient in reading, they will not be able to compete in the modern world. If high school graduates are deficient in writing, they will not be able to compete in the modern world. Th erefore, if high school graduates are defi cient in reading, then they are defi
★4. If there are dried-up riverbeds on Mars, then water once flowed on the Martian surface. Th ere are dried-up riverbeds on Mars. Th erefore, water once fl owed on the Martian surface. Translate the following arguments into symbolic form. Th en determine whether each is valid or invalid by
3. If fossil fuel combustion continues at its present rate, then a greenhouse eff ect will occur. If a greenhouse eff ect occurs, then world temperatures will rise.Th erefore, if fossil fuel combustion continues at its present rate, then world temperatures will rise. Translate the following
2. Brazil has a huge foreign debt. Therefore, either Brazil or Argentina has a huge foreign debt. Translate the following arguments into symbolic form. Th en determine whether each is valid or invalid by constructing a truth table for each.
★1. If national elections deteriorate into TV popularity contests, then smoothtalking morons will get elected. Th erefore, if national elections do not deteriorate into TV popularity contests, then smooth-talking morons will not get elected. Translate the following arguments into symbolic form.
★10. Nicole Evans expresses her philosophy as follows: “If the mind is identical to the brain, then personal freedom does not exist and humans are not responsible for their actions. If personal freedom does not exist, then the mind is identical to the brain. Either humans are responsible for
9. Cindy, Jane, and Amanda witnessed a bank robbery. At trial, Cindy testifi ed that Left y did not enter the bank, and if Howard pulled a gun, then Conrad collected the money. Jane testifi ed that if Howard did not pull a gun, then Left y entered the bank. Amanda testifi ed that if Conrad
8. Eric Carson sums up his beliefs about God as follows: “God exists if and only if either life is meaningful or the soul is not immortal. God exists and the soul is immortal. If God exists, then life is not meaningful.” Is it possible that Eric’s beliefs make sense?
★7. Two stockbrokers are having a discussion. One claims that Netmark will introduce a new product if and only if both Datapro cuts its work force and Compucel expands production. The other claims that Datapro will cut its work force, and Compucel will expand production if and only if Netmark
6. Automotive expert Frank Goodbody has this to say about Japanese imports:“If Mitsubishi is the sportiest, then both Toyota is the most trouble-free and Isuzu is not the lowest priced. If Isuzu is the lowest priced, then both Toyota is not the most trouble-free and Mitsubishi is the
5. Antonia Martinez, who is running for the state senate, makes this statement:“Either a tax reduction is feasible only if both educational costs do not increase and the welfare program is abolished, or a tax reduction is feasible and either the welfare program will not be abolished or
★4. Two astronomers are discussing supernovas. Dr. Frank says, “Research has established that if a supernova occurs within ten light years of the earth, then life on earth will be destroyed.” Dr. Harris says, “Research has also established that either a supernova will not occur within ten
3. Christina and Th omas are having a discussion about their plans for the evening.Christina: “If you don’t love me, then I’m certainly not going to have sex with you.” Th omas: “Well, that means that if I do love you, then you will have sex with me, right?” Is Th omas correct? (Hint:
2. A high school principal made this statement to the school board: “Either music is not dropped from the curriculum or the students will become cultural philistines; furthermore, the students will not become cultural philistines if and only if music is dropped from the curriculum.” Assuming
★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
15. Q ⊃ ∼(K ∨ F) (K • Q) ∨ (F • Q) 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,
14. Z • (C ≡ P) C ≡ (Z • ∼P) 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
★13. H • (K ∨ J) (J • H) ∨ (H • K) 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,
12. R • (Q ∨ S) (S ∨ R) • (Q ∨ R) 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
11. G • (E ∨ P) ∼(G • E) • ∼(G • P) 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;
★10. W ≡ (B • T) W • (T ⊃ ∼B) 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
9. M ⊃ (K ⊃ P) (K • M) ⊃ P 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
8. N • (A ∨ ∼E) ∼A • (E ∨ ∼N) 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
★7. (E ⊃ C) ⊃ L E ⊃ (C ⊃ L) 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
6. H ≡ ∼G (G • H) ∨ (∼G • ∼H) 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
5. ∼A ≡ X (X • ∼A) ∨ (A • ∼X) 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
★4. R ∨ ∼S S • ∼R 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
3. ∼K ⊃ L K ⊃ ∼L 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
2. F • M ∼(F ∨ M) 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
★1. ∼D ∨ B ∼(D • ∼B) 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
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