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logic functions and equations

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

6. All of the operas except Mozart’s were well performed, and Carmen was not written by Mozart. In the following enthymemes determine whether the missing statement is a premise or a conclusion. Then supply the missing statement, attempting whenever possible to convert the enthymeme into a valid
5. Only nonprofi t organizations are exempt from paying taxes, so churches must be exempt. In the following enthymemes determine whether the missing statement is a premise or a conclusion. Then supply the missing statement, attempting whenever possible to convert the enthymeme into a valid
★4. A few fraternities have dangerous initiation rites, and those that do have no legitimate role in campus life. In the following enthymemes determine whether the missing statement is a premise or a conclusion. Then supply the missing statement, attempting whenever possible to convert the
3. Carrie Underwood is a talented singer. Aft er all, she’s won several Grammy awards. In the following enthymemes determine whether the missing statement is a premise or a conclusion. Then supply the missing statement, attempting whenever possible to convert the enthymeme into a valid argument.
2. Any form of cheating deserves to be punished, and plagiarism is a form of cheating. In the following enthymemes determine whether the missing statement is a premise or a conclusion. Then supply the missing statement, attempting whenever possible to convert the enthymeme into a valid argument. Th
★1. Some police chiefs undermine the evenhanded enforcement of the law, because anyone who fi xes parking tickets does that. In the following enthymemes determine whether the missing statement is a premise or a conclusion. Then supply the missing statement, attempting whenever possible to convert
15. Autistic children are occasionally helped by aversive therapy. But aversive therapy is sometimes inhumane. Th us, autistic children are sometimes helped by inhumane therapy. Translate the following arguments into standard-form categorical syllogisms, then use Venn diagrams or the rules for
14. All of the movies except the chick fl icks were exciting. Hence, the action fi lms were exciting, because none of them is a chick fl ick. Translate the following arguments into standard-form categorical syllogisms, then use Venn diagrams or the rules for syllogisms to determine whether each is
★13. Diseases carried by recessive genes can be inherited by off spring of two carriers.Th us, since cystic fi brosis is a disease carried by recessive genes, it can be inherited by off spring of two carriers. Translate the following arguments into standard-form categorical syllogisms, then use
12. According to surveys, there are college students who think that Africa is in North America. But anyone who thinks that has no knowledge of geography.It follows that there are college students who have no knowledge of geography. Translate the following arguments into standard-form categorical
11. 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. Translate the following arguments into standard-form categorical syllogisms, then use Venn diagrams or the rules for syllogisms
★10. TV viewers cannot receive scrambled signals unless they have a decoder.Whoever receives digital satellite signals receives scrambled signals. Th erefore, whoever receives digital satellite signals has a decoder. Translate the following arguments into standard-form categorical syllogisms,
9. If a marriage is based on a meshing of neuroses, it allows little room for growth.If a marriage allows little room for growth, it is bound to fail. Th erefore, if a marriage is based on a meshing of neuroses, it is bound to fail. Translate the following arguments into standard-form categorical
8. Not all interest expenses are tax deductible. Home mortgage payments are interest expenses. Th us, they are not tax deductible. Translate the following arguments into standard-form categorical syllogisms, then use Venn diagrams or the rules for syllogisms to determine whether each is valid or
★7. Shania Twain sings what she wants. Hence, since Shania sings country songs, it follows that she must want to sing country songs. Translate the following arguments into standard-form categorical syllogisms, then use Venn diagrams or the rules for syllogisms to determine whether each is valid
6. Any city that has excellent art museums is a tourist destination. Th erefore, Paris is a tourist destination, because it has excellent art museums. Translate the following arguments into standard-form categorical syllogisms, then use Venn diagrams or the rules for syllogisms to determine whether
5. There are public schools that teach secular humanism. Therefore, since secular humanism is a religion, there are public schools that teach religion. Translate the following arguments into standard-form categorical syllogisms, then use Venn diagrams or the rules for syllogisms to determine
★4. Whoever wrote the Declaration of Independence had a big impact on civilization, and Th omas Jeff erson certainly had that. Th erefore, Th omas Jeff erson wrote the Declaration of Independence. Translate the following arguments into standard-form categorical syllogisms, then use Venn diagrams
3. Environmentalists purchase only fuel-effi cient cars. Hence, Hummers must not be fuel effi cient, since environmentalists do not purchase them. Translate the following arguments into standard-form categorical syllogisms, then use Venn diagrams or the rules for syllogisms to determine whether
2. Whenever suicide rates decline, we can infer that people’s lives are better adjusted. Accordingly, since suicide rates have been declining in recent years, we can infer that people’s lives have been better adjusted in recent years. Translate the following arguments into standard-form
★1. Physicists are the only scientists who theorize about the nature of time, and Stephen Hawking certainly does that. Th erefore, Stephen Hawking must be a physicist. Translate the following arguments into standard-form categorical syllogisms, then use Venn diagrams or the rules for syllogisms
★10. Some foreign emissaries are people without diplomatic immunity, so some people invulnerable to arrest and prosecution are foreign emissaries, because no people with diplomatic immunity are people vulnerable to arrest and prosecution. Rewrite the following arguments using letters to represent
9. No cases of AIDS are infections easily curable by drugs, since all diseases that infect the brain are infections not easily curable by drugs, and all diseases that do not infect the brain are cases other than AIDS. Rewrite the following arguments using letters to represent the terms, reduce the
8. All schools driven by careerism are institutions that do not emphasize liberal arts. It follows that some universities are not institutions that emphasize liberal arts, for some schools that are not driven by careerism are universities. Rewrite the following arguments using letters to represent
★7. Some proposed fl ights to Mars are inexpensive ventures, because all unmanned space missions are inexpensive ventures, and some proposed fl ights to Mars are not manned space missions. Rewrite the following arguments using letters to represent the terms, reduce the number of terms, and put
6. No objects that sink in water are chunks of ice, and no objects that fl oat in water are things at least as dense as water. Accordingly, all chunks of ice are things less dense than water. Rewrite the following arguments using letters to represent the terms, reduce the number of terms, and put
5. All aircraft that disintegrate in fl ight are unsafe planes. Th erefore, no poorly maintained aircraft are safe planes, because all well-maintained aircraft are aircraft that remain intact in fl ight. Rewrite the following arguments using letters to represent the terms, reduce the number of
★4. Some unintentional killings are not punishable off enses, inasmuch as all cases of self-defense are unpunishable off enses, and some intentional killings are cases of self-defense. Rewrite the following arguments using letters to represent the terms, reduce the number of terms, and put the
3. All Peace Corps volunteers are people who have witnessed poverty and desolation, and all people insensitive to human need are people who have failed to witness poverty and desolation. Thus, all Peace Corps volunteers are people sensitive to human need. Rewrite the following arguments using
2. Some people who do not regret their crimes are convicted murderers, so some convicted murderers are people insusceptible of being reformed, since all people susceptible of being reformed are people who regret their crimes. Rewrite the following arguments using letters to represent the terms,
★1. Some intelligible statements are true statements, because all unintelligible statements are meaningless statements and some false statements are meaningful statements. Rewrite the following arguments using letters to represent the terms, reduce the number of terms, and put the arguments into
10. true or false. If a syllogism breaks only Rule 5 and its three terms are “elves,” “trolls,” and“gnomes,” then the syllogism is valid from the Aristotelian standpoint.
9. true or false. If a syllogism breaks only Rule 5 and its three terms are “dogs,” “cats,” and“animals,” then the syllogism is valid from the Aristotelian standpoint.
8. true or false. If a syllogism breaks only Rule 5 and its three terms are “dogs,” “cats,” and “animals,”then the syllogism is valid from the Boolean standpoint.
7. true or false. If a valid syllogism has an E statement as a premise, then its conclusion can be an A statement.
6. true or false. If a valid syllogism has an O statement as its conclusion, then its premises can be an A and an I statement.
5. true or false. If a syllogism has an I statement as its conclusion, then Rule 2 cannot be violated.
4. I true or false. f a syllogism has an E and an O statement as premises, then no conclusion follows validly.
3. true or false. If a syllogism has two I statements as premises, then it is invalid.
2. true or false. If a valid syllogism has an E statement as its conclusion, then both the major and minor terms must be distributed in the premises.
1. true or false. If a categorical syllogism violates one of the first four rules, it may still be valid.
★10. All successful fl irts are masters at eye contact.All masters at eye contact are people genuinely interested in others.Th erefore, some people genuin ely interested in others are successful fl irts. Use the fi ve rules to determine whether the following standard-form syllogisms are valid
9. All inside traders are people subject to prosecution.Some executives with privileged information are not people subject to prosecution.Th erefore, some executives with privileged information are inside traders. Use the fi ve rules to determine whether the following standard-form syllogisms are
8. All war zones are places where abuse of discretion is rampant.Some places where abuse of discretion is rampant are international borders.Th erefore, some international borders are war zones. Use the fi ve rules to determine whether the following standard-form syllogisms are valid from the
★7. No searches based on probable cause are violations of Fourth Amendment rights.Some warrantless searches are violations of Fourth Amendment rights.Th erefore, some warrantless searches are not searches based on probable cause. Use the fi ve rules to determine whether the following
6. All members of the National Rifle Association are people opposed to gun control.All members of the National Rifl e Association are law-abiding citizens.Th erefore, all law-abiding citizens are people opposed to gun control. Use the fi ve rules to determine whether the following standard-form
5. All transparent metals are good conductors of heat.All transparent metals are good conductors of electricity.Th erefore, some good conductors of electricity are good conductors of heat. Use the fi ve rules to determine whether the following standard-form syllogisms are valid from the Boolean
★4. Some cases of affi rmative action are not measures justifi ed by past discrimination.No cases of affi rmative action are illegal practices.Therefore, some illegal practices are not measures justified by past discrimination. Use the fi ve rules to determine whether the following standard-form
3. No endangered species are creatures loved by the timber industry.All spotted owls are endangered species.Th erefore, some spotted owls are not creatures loved by the timber industry. Use the fi ve rules to determine whether the following standard-form syllogisms are valid from the Boolean
2. No individuals sensitive to the diff erence between right and wrong are people who measure talent and success in terms of wealth.All corporate takeover experts are people who measure talent and success in terms of wealth.Therefore, no corporate takeover experts are individuals sensitive to the
★1. Some nebulas are clouds of gas.Some clouds of gas are objects invisible to the naked eye.Th erefore, some objects invisible to the naked eye are nebulas. Use the fi ve rules to determine whether the following standard-form syllogisms are valid from the Boolean standpoint, valid from the
11. Reconstruct the following syllogistic forms and use the fi ve 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 fulfi
10. If, in a completed diagram, three areas of a single circle are shaded, but the argument is not valid from the Boolean standpoint, then it must be valid from the Aristotelian standpoint. True or False.
9. If, in a completed diagram, three areas of a single circle are shaded, and placing a circled X in the one remaining area would make the conclusion true, then the argument is valid from the Aristotelian standpoint but not from the Boolean standpoint. True or False.
8. If the conclusion is in the form “All S are P,” and inspection of the diagram reveals that the part of the S circle that is outside the P circle is shaded, then the argument is valid. True or False.
7. If the conclusion asserts that a certain area contains an X and inspection of the diagram reveals that only half an X appears in that area, the argument is valid. True or False.
6. If the conclusion asserts that a certain area is shaded, and inspection of the diagram reveals that only half that area is shaded, the argument is valid. True or False.
5. If a completed diagram contains two X’s, the argument cannot be valid. True or False.
4. When representing a universal statement in a Venn diagram, one always shades two of the seven areas in the diagram (unless one of these areas is already shaded). True or False.
3. If an X lies on the arc of a circle, the argument cannot be valid. True or False.
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 that the arc separates. True or False.
1. In the use of Venn diagrams to test the validity of syllogisms, marks are sometimes entered in the diagram for the conclusion. True or False.
21. 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 conclusion.” *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
20. Some snowfl akes are not uniform solids.All snowfl akes are six-pointed crystals.Th erefore, some six-pointed crystals are not uniform solids. Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid from the Boolean standpoint, valid from the
★19. No theocracies are regimes open to change.All theocracies are governments that rule by force.Therefore, some governments that rule by force are not regimes open to change. Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid from the Boolean
18. No spurned lovers are Valentine’s Day fanatics.Some moonstruck romantics are Valentine’s Day fanatics.Th erefore, some moonstruck romantics are not spurned lovers. Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid from the Boolean
17. All survivalists are people who enjoy simulated war games.No people who enjoy simulated war games are soldiers who have tasted the agony of real war.Th erefore, all soldiers who have tasted the agony of real war are survivalists. Use Venn diagrams to determine whether the following
★16. All currently living dinosaurs are giant reptiles.All giant reptiles are ectothermic animals.Th erefore, some ectothermic animals are currently living dinosaurs. Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid from the Boolean standpoint,
15. Some communications satellites are rocket-launched failures.All communications satellites are devices with antennas.Th erefore, some devices with antennas are rocket-launched failures. Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid from the
14. Some individuals who risk heart disease are people who will die young.Some smokers are individuals who risk heart disease.Th erefore, some smokers are people who will die young. Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid from the Boolean
★13. No people who profit from the illegality of their activities are people who want their activities legalized.All drug dealers are people who profi t from the illegality of their activities.Th erefore, no drug dealers are people who want their activities legalized. Use Venn diagrams to
12. All supernovas are objects that emit massive amounts of energy.All quasars are objects that emit massive amounts of energy.Th erefore, all quasars are supernovas. Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid from the Boolean standpoint,
11. All circular triangles are plane fi gures.All circular triangles are three-sided fi gures.Th erefore, some three-sided fi gures are plane fi gures. Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid from the Boolean standpoint, valid from the
★10. No corporations that defraud the government are organizations the government should deal with.Some defense contractors are not organizations the government should deal with.Th erefore, some defense contractors are not corporations that defraud the government. Use Venn diagrams to determine
9. Some ATM locations are places criminals lurk.All places criminals lurk are places to avoid at night.Th erefore, some places to avoid at night are ATM locations. Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid from the Boolean standpoint, valid
8. Some individuals prone to violence are not men who treat others humanely.Some police offi cers are individuals prone to violence.Th erefore, some police offi cers are not men who treat others humanely. Use Venn diagrams to determine whether the following standard-form categorical syllogisms are
★7. No pediatricians are individuals who jeopardize the health of children.All faith healers are individuals who jeopardize the health of children.Th erefore, no faith healers are pediatricians. Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid
6. All impulse buyers are consumers with credit cards.All shopaholics are impulse buyers.Th erefore, all shopaholics are consumers with credit cards. Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid from the Boolean standpoint, valid from the
5. No engineering majors are candidates for nightly hookups.No candidates for nightly hookups are deeply emotional individuals.Th erefore, no deeply emotional individuals are engineering majors. Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid from
★4. All high-fat diets are diets high in cholesterol.Some diets high in cholesterol are not healthy food programs.Th erefore, some healthy food programs are not high-fat diets. Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid from the Boolean
3. No individuals truly concerned with the plight of suffering humanity are people motivated primarily by self-interest.All television evangelists are people motivated primarily by self-interest.Therefore, some television evangelists are not individuals truly concerned with the plight of suff ering
2. No AIDS victims are people who pose an immediate threat to the lives of others.Some kindergarten children are AIDS victims.Th erefore, some kindergarten children are not people who pose an immediate threat to the lives of others. Use Venn diagrams to determine whether the following standard-form
★1. All corporations that overcharge their customers are unethical businesses.Some unethical businesses are investor-owned utilities.Th erefore, some investor-owned utilities are corporations that overcharge their customers. Use Venn diagrams to determine whether the following standard-form
10. Th e conditionally valid syllogistic forms are invalid if the requisite condition is not fulfi lled. True or False.
9. Th e unconditionally valid syllogistic forms are valid from both the Boolean and the Aristotelian standpoints. True or False.
8. In a standard-form syllogism having Figure 2, the two occurrences of the middle term are on the right. True or False.
7. To determine its mood and fi gure, a categorical syllogism must fi rst be put into standard form. True or False.
6. The major premise of a standard-form categorical syllogism contains the subject of the conclusion. True or False.
5. In a standard-form categorical syllogism the two occurrences of each term must be identical. True or False.
4. Th e statements in a standard-form categorical syllogism need not be expressed in standard form. True or False.
3. Th e statements in a categorical syllogism need not be expressed in standard form. True or False.
2. Some categorical syllogisms cannot be put into standard form. True or False.
1. Every syllogism is a categorical syllogism. True or False. True or False.
11. Reconstruct the syllogistic forms from the following combinations of mood and fi gure.★1. OAE-3★2. EIA-4★3. AII-3★4. IAE-1★5. AOO-2★6. EAO-4★7. AAA-1★8. EAO-2★9. OEI-3★10. OEA-4
★10. Some silicates are crystalline substances, because all silicates are oxygen compounds, and some oxygen compounds are not crystalline substances. Put the following syllogisms into standard form, using letters to represent the terms, and name the mood and fi gure. Th en use the two lists of
9. No people who respect human life are terrorists, and all airline hijackers are terrorists. Hence, no airline hijackers are people who respect human life. Put the following syllogisms into standard form, using letters to represent the terms, and name the mood and fi gure. Th en use the two lists
8. Some racists are not people suited to be immigration officials, given that some humanitarians are not people suited to be immigration offi cials, and no humanitarians are racists. Put the following syllogisms into standard form, using letters to represent the terms, and name the mood and fi
★7. All pranksters are exasperating individuals, consequently some leprechauns are exasperating individuals, since all leprechauns are pranksters. Put the following syllogisms into standard form, using letters to represent the terms, and name the mood and fi gure. Th en use the two lists of valid
6. Some African nations are not countries deserving military aid, because some African nations are not upholders of human rights, and all countries deserving military aid are upholders of human rights. Put the following syllogisms into standard form, using letters to represent the terms, and name
5. No illegal aliens are people who have a right to welfare payments, and some migrant workers are illegal aliens. Thus, some people who have a right to welfare payments are migrant workers. Put the following syllogisms into standard form, using letters to represent the terms, and name the mood and

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