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logic functions and equations
A Concise Introduction To Logic 12th Edition Patrick J. Hurley - Solutions
After researching one of the following topics, write an essay of eight to ten pages evaluating the plausibility of the underlying hypothesis.1. The existence of UFOs 2. Extraterrestrial abductions 3. Scientific creationism 4. Darwin’s theory of natural selection 5. Biorhythms 6. Phrenology 7.
Design or perform the following experiments, as directed.1. Psychic phenomena include psychokinesis, telepathy, clairvoyance, and precognition(see Exercise I, 7). Design an experiment to test for the existence of one or more forms of these phenomena. The experiment might use Zener cards, dice,
On June 24 and 26, 1981, six children in the little village of Medjugorje in Bosnia(former Yugoslavia) claimed to have had a vision of the Virgin Mary. In the days and weeks that followed, more alleged visions occurred, and reports began to attract visitors anxious for a vision of their own. From
In 1955, the psychologist N. D. Sundburg gave the Minnesota Multiphasic Personality Inventory, a commonly used personality test, to forty-four students.Next he had two highly experienced psychologists draw up personality sketches for each student based on the results of the test. He then presented
The first step in providing an astrological reading is to cast the chart. This is followed by an analysis of interacting chart factors, which in turn is followed by the astrologer’s interpretation of these factors. In regard to the third step, D. Hamblin, former chairman of the United Kingdom
On the basis of a person’s natal chart (horoscope cast according to the person’s date, time, and place of birth), astrologers claim to be able to analyze that person’s character and personality and make predictions about his or her life course. To test the claims of astrology about character
In 1970, the physicist David Simpson and his colleague Norman Foxwell performed an experiment involving a group of UFO buffs in England. On a Saturday evening about thirty of these individuals had gathered on a remote hilltop where they thought there was a good chance of sighting a UFO. Simpson
In 1975 James Randi offered $10,000 (later increased to $1,000,000) to any person who could perform a paranormal feat (including any demonstration of psychic power) in his presence under controlled conditions. (This offer was still open as of the printing of this book.) Since that time, hundreds of
Psychic phenomena include psychokinesis, telepathy, clairvoyance, and precognition.Psychokinesis is the ability to move objects through the direct power of the mind, telepathy is the power to perceive the thoughts of others without the use of the senses, clairvoyance is the ability to perceive
Suppose you are a fortune-teller. You have a small shop in Milwaukee complete with a crystal ball, beads hanging in the doorway, incense, and a shelf of books devoted to the dark arts. At about 4:00 in the afternoon in early March a couple in their mid-thirties comes into your shop. They are
The modern creationist theory, called “scientific creationism,” propounded by Duane Gish and Henry Morris, accounts for geologic formations and fossils by appealing to the great flood of Noah. This flood allegedly killed numerous mammals, birds, fish, and insects, and their carcasses settled in
One of the early creationist theories advanced in opposition to Darwin’s theory of natural selection was put forward by the nineteenth-century naturalist Philip Gosse. According to this theory, God created the world in about 4000 b.c., and he did so in exactly six days, per the account in
Discuss the following reports from residents of Hong Kong (taken from “Hong Kong’s Feng Shui: Popular Magic in a Modern Urban Setting,” by Charles F.Emmons, Journal of Popular Culture, Summer 1992).a. I have a little restaurant in Aberdeen, a seafood place facing the sea. I used to be on the
Discuss the meaning of the following selections:a. The universe is a macrocosm of creative energy and power, and every man, woman, and child is the epitome of this totality of the cosmos. Within your individualized energy field, the microcosm called you, are twenty-two Causal Powers, or angels,
Discuss the evidentiary problems raised by the following questions:a. After drinking tea made from tarragon leaves every day for a year, your grandfather reports that his bunions cleared up. Does this prove that tarragon tea has the power to cure bunions?b. You go to a psychotherapist who diagnoses
Answer “true” or “false” to the following statements:★1. Hypothetical reasoning is useful when the evidence by itself does not provide the solution to the problem.2. Hypotheses are derived directly from the evidence.3. Hypotheses serve the purpose of directing the search for additional
Write a short paper (2–3 pages) analyzing one or more of the hypotheses formulated by Sherlock Holmes in one of the stories by Arthur Conan Doyle. Include a discussion of the problem, the hypothesis, the implications that were drawn, and the test procedures.
Write a short paper (3–5 pages) on one of the following scientific events. Discuss the problem, one or more hypotheses that were formulated, the implications that were drawn, and the test procedures that were used. Then evaluate the hypothesis in terms of adequacy, internal coherence, external
The following article was written by a physician in the emergency room of a hospital.*The article describes the difficulty that the author and other physicians faced in diagnosing the nature of a patient’s illness. Identify the problem, the hypotheses suggested, the implications drawn, and the
For each of the following situations, invent at least three hypotheses aimed at explaining what went wrong or at solving the problem. Then, for each hypothesis, describe one or more experiments or inquiries that would confirm or disconfirm the hypothesis.1. Someone you have been dating has a
Answer “true” or “false” to the following statements:★1. If a sample is very large, it need not be randomly selected.2. If a population is randomly arranged, a sample obtained by selecting every tenth member would be a random sample.3. If a sample is randomly selected, the larger the
Compute the answers to the following questions:★1. What figures should be written in the left-hand column of Table 12.1, in the text, to produce a similar table based on a confidence level of 99 percent? For a confidence level of 99 percent, the margin of error is approximately equal to
Criticize the following arguments in light of the material presented in this chapter.★1. To test the algae content in a lake, a biologist took a sample of the water at one end. The algae in the sample registered 5 micrograms per liter. Therefore, the algae in the lake at that time registered 5
20. Mr. Andrews, a grape merchant, inquires about a certain wine that he tastes at a party. The host tells him that from a total of ten bottles of that wine, six came from the north vineyard and four came from the south vineyard. From this information, the merchant concludes that he should visit
Ms. Jones, a bookstore owner, wishes to send out an advertisement to potential customers. She estimates that 20 percent of the town’s residents are recreational readers, and she knows that all of the residents are either recreational readers or TV addicts (but not both). Also, a media expert has
18. A physician has diagnosed a patient as having either hepatitis or liver cancer(but not both). Statistics reveal that hepatitis occurs in the general population twice as frequently as liver cancer. Thus, the physician tentatively concludes that the patient probably has hepatitis. Later the
17. Knowing that your friend Angella studies for her tests only 40 percent of the time, you place an even bet with a third party that Angella will not study for her upcoming test. Later, you just happen to hear that Angella passed the test.Should you retract your bet? Assume that Angella passes
★16. We are given three new urns each containing seven red, five green, and three white balls, and two old urns each containing five red, three green, and seven white balls. The urns are identical except for an old or new date stamped beneath the base. If a single red ball is randomly drawn from
15. Assign a numerical value to the strength of the following argument: The Wilson family has four children. Therefore, at least two of the children were born on the same day of the week.
14. Assign a numerical value to the strength of the following argument: The odds are 5 to 3 that the Indians will win the American League pennant and 7 to 5 that the Cardinals will win the National League pennant. Therefore, the Indians and the Cardinals will meet in the World Series.
★13. The probability of a twenty-year-old man living to age seventy is .74, and the probability of a twenty-year-old woman living to the same age is .82. If a recently married couple, both age twenty, give 8 to 1 odds on their staying married for fifty years, what is the probability thata. At
12. What is the probability of drawing an ace and a king on three draws (without replacement) from a poker deck? (Hint: Use the negation rule.)
11. What is the probability of drawing either an ace or a king (or both) on three draws (without replacement) from a poker deck? (Hint: Use the negation rule.)
★10. Given an urn containing three red, four green, and five yellow balls, if two balls are drawn from the urn (without replacement), what is the probability thata. Both are red?b. One is green, the other yellow?c. One is either red or green?d. At least one is green?e. Both have the same color?
9. Given two urns, one containing two red, three green, and four yellow balls, the other containing four red, two green, and three yellow balls, if a single ball is drawn from each urn, what is the probability thata. Both are red?b. At least one is green?c. One is red, the other yellow?d. At least
6. What is the probability of getting at least one head on three tosses of a coin?★7. What is the probability of getting at least one 6 on three rolls of a die?8. If a pair of dice are rolled, what is the probability that the points add up toa. 5?b. 6?c. 7?
5. What is the probability of drawing at least one ace from a poker deck on two draws if the first card is replaced before the second is drawn?
★4. What is the probability of drawing two aces from a poker deck in two drawsa. If the first card is replaced before the second is drawn?b. If the first card is not replaced before the second is drawn?
3. What is the probability of drawing either a king or a queen from a poker deck(no jokers) on a single draw?
2. What is the probability of getting heads on three successive tosses of a coin?
What is the probability of getting either a six or a one from a single roll of a die?
Compute probabilities or odds for the following simple events.★1. What is the probability of rolling a five on a single roll of a die? What are the odds for this event?2. From a sample of 9,750 Ajax trucks, 273 developed transmission problems within the first two years of operation. What is the
Identify the cause suggested by the information presented in the following tables.Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition? Can you identify the method? *1. Possible Conditions Occurrence A B C D E Phenomenon * * * * 2 * * * * 3 * * 4 * *
15. A cosmetics manufacturer tested a new cleansing cream on forty rabbits. The rabbits were virtually the same genetically and were the same age. Twenty of the rabbits were randomly placed in the experimental group and the other twenty were placed in the control group. A patch containing the cream
14. A sociologist conducted a study to determine if a correlation exists between grade point average at the time of graduation and income ten years after graduation. The sociologist visited the alumni office of a local university and obtained the names and addresses of those who had graduated ten
★13. Two of Mr. Andrews’s rose bushes became infected with aphids. Mr. Andrews proceeded to spray one of the bushes with malathion insecticide but left the other bush untouched. The two bushes are both American Beauty, are five years old, have virtually identical locations, receive the same
12. A doctor has five patients who suffer from an unusual form of cancer. The patients are distinguished by the following living conditions. Davis, Jones, and Ellis live in a smoggy area near high-tension power lines, and Smith and Frank smoke cigarettes and live downwind from a company that
11. A metallurgist added eight substances in various combinations to seven samples of molten aluminum for the purpose of producing aluminum alloys. The metallurgist was interested in producing an alloy that had a special resistance to corrosion. The samples were distinguished by the following
★10. A psychiatrist had six adult women patients who suffered blurred ego boundaries.These patients were distinguished by the following characteristics. Meg and Sue had been subjected to corporal punishment as children and both had siblings. Dot and Jane were adopted, had a male parent figure,
9. A man developed an allergic reaction to an unknown food. His doctor asked him about foods that often cause allergic reactions, and the man replied that he had eaten coconut, chocolate, nuts, milk products, shellfish, peppers, eggs, and wheat products prior to suffering the reaction. The doctor
8. From a comparison of statistics a criminologist detected what he thought was a correlation between fluctuations in the employment rate and in crimes of theft. For every 2 percent increase in the employment rate, the rate of theft decreased by 1 percent, and for every 2 percent decrease in the
★7. Mrs. Wilkins sometimes has trouble sleeping. In order to determine the cause, she decided to take note of her pre-bedtime behavior over the course of a week. On Monday she drank chamomile tea, had a late dinner, took a hot bath, read from a book, took a walk, and slept well. On Tuesday she
6. Nancy was contemplating the purchase of a new oven for her kitchen, but she could not decide between an electric or a gas unit. Thus, she decided to conduct an experiment using the ovens—one gas, one electric—of two friends who live in adjoining apartments. She mixed up two identical batches
5. A manufacturer of fishing equipment conducted a test of its products by giving them to eight fishermen who used them with the following results. Ed and Flo used a Hot Spot lure and caught no fish. Dan and Amy used a Trusty rod with a Husky reel, and Amy caught fish but Dan did not. Jake used a
★4. The repair manager for a manufacturer of desktop computers noticed that a large number of units were being returned for repairs. The manager selected a sample of seven returned units and noticed that these units were distinguished by the following characteristics. Units 1 and 3 had type X
3. An administrator for the Internal Revenue Service noticed that tax revenues for a certain year were down by 14 percent. Of this amount, the administrator attributed 6 percent to an economic slowdown that year, 3 percent to higher interest rates that led to higher write-offs, and 2 percent to
2. An eighth-grade teacher had five pupils who read very well. These pupils were distinguished by the following features. Tom came from a large family, had professional parents who were not wealthy, had training in phonics, read novels, lived close to a library, and watched educational TV. Andy
★1. To determine the effectiveness of an oil additive, a testing firm purchased two cars of the same make, year, and model, and drove each a distance of 30,000 miles using the same kind of gasoline, the same kind of oil, the same driver, under the same road conditions. The oil in one engine
Identify the kind of causality intended by the following statements. Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition?★1. Throwing a brick through a window will cause the window to break.2. Heating an iron rod causes it to expand.3. Slashing an
15. During fifteen years of marriage, James and Leslie Knox had not succeeded in having a baby. As a last resort, they tried in vitro fertilization. Doctors surgically removed nine eggs from Leslie and fertilized them with James’s sperm. The embryos were then placed in a freezer until the proper
14. Lynn Dodd, age twenty, has become a member of New Age Enlightenment, a religious cult group. The group has convinced Lynn to sell all her worldly possessions and give the proceeds to the group. The group forbids any contact between Lynn and her relatives and friends. On one occasion Lynn’s
★13. A negligent person who causes an injury to another person is liable for the latter’s injuries. Because it is sometimes very difficult to determine the causal extent of a negligent action, courts have developed the theory of proximate cause, which limits the scope of liability. In this
12. Constructive eviction is a legal doctrine by which a landlord who substantially interferes with a tenant’s use and enjoyment of the premises will be considered to have evicted the tenant. Such a landlord cannot collect rent from the tenant.In this connection, Isabel signed a lease for an
11. The First Amendment to the U.S. Constitution states that Congress shall make no law abridging the freedom of speech or the right to peaceable assembly.This “law” applies to states (and cities) as a result of the adoption of the Fourteenth Amendment. In reliance on the First Amendment, a
★10. The Fourth Amendment to the U.S. Constitution prohibits unreasonable searches and seizures. A search is defined as a “violation of a person’s reasonable expectation of privacy by the police.” Legal issues dealing with searches often turn on the question of whether the person who was
9. According to the doctrine of adverse possession, a person occupying a piece of land in a way that is open, notorious, and hostile to the owner’s rights can claim ownership of the land after a certain number of years of continuous occupancy.In this connection, Dr. Wacko, a mad scientist, hauled
8. Andrew is thinking about buying stock in E-Tron, a new company that sells electronic equipment over the Internet. Six months ago, he bought shares in E-Boot, a new company that sells shoes over the Internet, and the price of the stock doubled in two months. Andrew argues that if he buys E-Tron,
★7. Laura is considering taking Calculus I from Professor Rogers. Her friend Gina took Professor Rogers for this class and got an A. Laura concludes that she, too, will get an A from Professor Rogers. How do the following facts bear on Laura’s argument?a. Gina earned straight A’s in high
6. Paul is searching for a puppy that will grow up to be friendly with his children.His friend Barbara has an Airedale terrier that is good with her children. From this, Paul concludes that an Airedale puppy would make a good choice. How do the following facts bear on Paul’s argument?a.
5. Susan is considering a job as public relations specialist with the Chamber of Commerce. Her friend Terry took such a job one year ago, and within nine months her annual salary was $50,000. Susan argues that if she takes this job, then her annual salary will be at least $50,000 within nine
★4. Sam has planned a one-day fishing trip in Alaska. He intends to fish off Rocky Point, where he fished last year. Because he caught five fish in a one-day outing last year, Sam concludes that he will catch five fish this year. How do the following facts bear on Sam’s argument?a. Last year
3. Kristin is president of a corporation that operates a chain of clothing stores, and she faces the task of hiring a manager to replace a man who retired from one of the stores. The former manager increased sales by 15 percent every year for the past five years. Kristin concludes that Roger
2. Harold needs to have his rugs cleaned, and his friend Veronica reports that Ajax Carpet Service did an excellent job on her rugs. From this, Harold concludes that Ajax will do an equally good job on his rugs. How do the following facts bear on Harold’s argument?a. Veronica hired Ajax several
★1. Jessica has long admired Rachel’s near-perfect body, and she notes that Rachel works out on a Roboflex exercise machine. Jessica concludes that if she buys a Roboflex for herself, she will be able to duplicate Rachel’s results. How do the following facts bear on Jessica’s argument?a.
Evaluate the arguments from analogy contained in the dialogue between Jason and Deirdre. First, identify the primary and secondary analogues in each analogy and counteranalogy. Next, list the similarities between the primary and secondary analogues and note their relevance to the conclusion. Add
Derive the conclusion of the following arguments. Use conditional proof or indirect proof as needed.★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
Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.★(1) 1. (x)(x = a)2. (∃x)Rx / Ra(2) 1. Ke 2. ∼Kn / e ≠ n(3) 1. (x)(x = c ⊃ Nx) / Nc★(4) 1. (∃x)(x = g)2. (x)(x = i) / g = i(5) 1. (x)(Gx ⊃ x = a)2. (∃x)(Gx Hx) / Ha(6) 1.
Translate the following statements.Simple identity statements★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 .
Translate the following arguments into symbolic form. Then derive the conclusion of each, using conditional proof or indirect proof when needed.★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
Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.★(1) 1. (x)[Ax ⊃ ( y)Bxy]2. Am / ( y)Bmy(2) 1. (x)[Ax ⊃ ( y)(By ⊃ Cxy)]2. Am Bn / Cmn(3) 1. (∃x)[Ax ( y)(By ⊃ Cxy)]2. (∃x)Ax ⊃ Bj / (∃x)Cxj★(4) 1. (x)(∃y)(Ax ⊃ By)
I. Translate the following statements into symbolic form.★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
Translate the following arguments into symbolic form. Then use either the counterexample method or the finite universe method to prove that each is invalid.★1. Violinists who play well are accomplished musicians. There are some violinists in the orchestra. Therefore, some musicians are
Use the finite universe method to prove that the following symbolized arguments are invalid.★(1) 1. (x)(Ax ⊃ Bx)2. (x)(Ax ⊃ Cx) / (x)(Bx ⊃ Cx)(2) 1. (x)(Ax ⋁ Bx)2. ∼An / (x)Bx(3) 1. (∃x)Ax ⋁ (∃x)Bx 2. (∃x)Ax / (∃x)Bx★(4) 1. (x)(Ax ⊃ Bx)2. (∃x)Ax / (x)Bx(5) 1. (x)[Ax ⊃
Use the counterexample method to prove that the following symbolized arguments are invalid.★(1) 1. (x)(Ax ⊃ Bx)2. (x)(Ax ⊃ ∼Cx) / (x)(Cx ⊃ Bx)(2) 1. (∃x)(Ax Bx)2. (x)(Cx ⊃ Ax) / (∃x)(Cx Bx)(3) 1. (x)(Ax ⊃ Bx)2. Bc / Ac★(4) 1. (∃x)(Ax Bx)2. (∃x)(Ax Cx) / (∃x)[Ax (Bx Cx)](5)
Translate the following arguments into symbolic form. Then use conditional or indirect proof to derive the conclusion of each.★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
Use either indirect proof or conditional proof to derive the conclusions of the following symbolized arguments.★(1) 1. (x)(Ax ⊃ Bx)2. (x)(Ax ⊃ Cx) / (x)[Ax ⊃ (Bx Cx)](2) 1. (∃x)Ax ⊃ (∃x)(Bx Cx)2. (∃x)(Cx ⋁ Dx) ⊃ (x)Ex / (x)(Ax ⊃ Ex)(3) 1. (∃x)Ax ⊃ (∃x)(Bx Cx)2.
Translate the following arguments into symbolic form. Then use the quantifier negation rule and the eighteen rules of inference to derive the conclusion of each. Do not use either conditional proof or indirect proof.★1. If all the physicians are either hematologists or neurologists, then there
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) 1. (x)Ax ⊃ (∃x)Bx 2. (x)∼Bx / (∃x)∼Ax(2) 1. (∃x)∼Ax ⋁ (∃x)∼Bx 2. (x)Bx /
III. The following dialogue contains nine arguments. Translate each into symbolic form and then use the eighteen rules of inference to derive the conclusion of each.Some of them are quite challenging.Where’s the Beef ?“Have you decided what to order?” Paul says to Mindy, as he folds his menu
Translate the following arguments into symbolic form. Then use the eighteen rules of inference to derive the conclusion of each. Do not use conditional or indirect proof.★1. Oranges are sweet. Also, oranges are fragrant. Therefore, oranges are sweet and fragrant. (O, S, F )2. Tomatoes are
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) 1. (x)(Ax ⊃ Bx)2. (x)(Bx ⊃ Cx) / (x)(Ax ⊃ Cx)(2) 1. (x)(Bx ⊃ Cx)2. (∃x)(Ax Bx) / (∃x)(Ax Cx)(3) 1. (x)(Ax ⊃ Bx)2. ∼Bm /
Translate the following statements into symbolic form. Avoid negation signs preceding quantifiers. The predicate letters are given in parentheses.★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
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 ⊃ Q) ⊃ [(P R) ⊃ (Q R)]5. (P ⋁ ∼Q) ⊃ [(∼P ⋁ R) ⊃ (Q ⊃ R)]6. P
Translate the following arguments into symbolic form, using the letters in the order in which they are listed. Then use indirect proof and the eighteen rules of inference to derive the conclusion of each. Having done so, attempt to derive the conclusion without using indirect proof.★1. If
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) 1. (S ⋁ T ) ⊃ ∼S / ∼S(2) 1.
Translate the following arguments into symbolic form, using the letters in the order in which they are listed. Then use conditional proof and the eighteen rules of inference to derive the conclusion of each. Having done so, attempt to derive the conclusion without using conditional proof.★1. If
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) 1. N ⊃ O 2. N ⊃ P / N ⊃ (O P)(2) 1. F ⊃ E 2. (F E ) ⊃ R / F ⊃ R(3) 1. G ⊃
The following dialogue contains ten arguments. Translate each into symbolic form and then use the eighteen rules of inference to derive the conclusion of each.Is This the End?Brian and Molly are at the memorial service of a mutual friend who had died suddenly the week before. “I’m still shocked
Translate the following arguments into symbolic form and then use the eighteen rules of inference to derive the conclusion of each. Use the translation letters in the order in which they are listed.★1. If sports-shoe manufacturers decline to use kangaroo hides in their products, then Australian
Use the eighteen rules of inference to derive the conclusions of the following symbolized arguments.★(1) 1. (S K ) ⊃ R 2. K / S ⊃ R(2) 1. T ⊃ (F ⋁ F )2. ∼(F F ) / ∼T(3) 1. G ⊃ E 2. H ⊃ ∼E / G ⊃ ∼H★(4) 1. S ≡ Q 2. ∼S / ∼Q(5) 1. ∼N ⋁ P 2. (N ⊃ P) ⊃ T / T(6) 1.
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