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logic functions and equations
A Concise Introduction To Logic 11th Edition Patrick J. Hurley - Solutions
3. Slashing an infl ated automobile tire with a knife will cause it to go fl at. Identify the kind of causality intended by the following statements. Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition?
2. Heating an iron rod causes it to expand. 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. Th rowing a brick through a window will cause the window to break. Identify the kind of causality intended by the following statements. Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition?
During fi ft een 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.Th e embryos were then placed in a freezer until the proper
Lynn Dodd, age twenty, has become a member of New Age Enlightenment, a religious cult group. Th e 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 diffi cult 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.Th is “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 defi ned as a “violation of a person’s reasonable expectation of privacy by the police.” Legal issues dealing with searches oft en 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,
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 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. Barbara’s dog
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 fi shing trip in Alaska. He intends to fi sh 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 fi ve fi sh this year. How do the following facts bear on Sam’s argument?a. Last
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. Th e former manager increased sales by 15 percent every year for the past fi ve 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
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. Th e former manager increased sales by 15 percent every year for the past fi ve 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 Robofl ex exercise machine. Jessica concludes that if she buys a Robofl ex for herself, she will be able to duplicate Rachel’s results. How do the following facts bear on Jessica’s argument?a.
★16. Every student except Charles and Norman passed the course. The only student who was dismissed was Norman. Every student retook the course if and only if he or she was not dismissed and did not pass. Charles is not Norman.Th erefore, exactly one student retook the course. (Sx: x is a student;
15. Every candidate except Mary was elected. Th e only candidate who was elected is Ralph. Mary is not Ralph. Th erefore, there were exactly two candidates. (Cx:x is a candidate; Ex: x was elected; m: Mary; r: Ralph) Derive the conclusion of the following arguments. Use conditional proof or
14. Th ere are at most two scientists in the laboratory. At least two scientists in the laboratory are Russians. No Russians are Chinese. Th erefore, if Norene is a Chinese scientist, then she is not in the laboratory. (Sx: x is a scientist; Lx: x is in the laboratory; Rx: x is Russian; Cx: x is
★13. Th ere are at least two attorneys in the offi ce. All attorneys are professionals.Th ere are at most two professionals in the offi ce. Th erefore, there are exactly two professionals in the offi ce. (Ax: x is an attorney; Ox: x is in the offi ce; Px: x is a professional) Derive the
12. Th e only dogs that barked were Fido and Pluto. Fido is not Pluto. Every dog except Fido ran on the beach. Th erefore, exactly one barking dog ran on the beach. (Dx: x is a dog; Bx: x barked; Rx: x ran on the beach; f: Fido; p: Pluto) Derive the conclusion of the following arguments. Use
11. Th ere are at least two philosophers in the library. Robert is the only French philosopher in the library. Th erefore, there is a philosopher in the library who is not French. (Px: x is a philosopher; Lx: x is in the library; Fx: x is French;r: Robert) Derive the conclusion of the following
★10. Th e tallest building in North America is the Willis Tower. Th e tallest building in North America is located in Chicago. If one thing is taller than another, then the latter is not taller than the former. Therefore, the Willis Tower is located in Chicago. (Bx: x is a building in North
9. Th e highest mountain is in Tibet. Th erefore, there is a mountain in Tibet that is higher than any mountain not in Tibet. (Mx: x is a mountain; Hxy: x is higher than y; Tx: x is in Tibet) Derive the conclusion of the following arguments. Use conditional proof or indirect proof as needed.
8. The only person who ordered fish is Astrid. The only person who suffered indigestion is Ms. Wilson. Some person who ordered fi sh also suff ered indigestion.Th erefore, Astrid is Ms. Wilson. (Px: x is a person; Ox: x ordered fi sh;Sx: x suff ered indigestion; a: Astrid; w: Ms. Wilson) Derive the
★7. Every member except Ellen sang a song. Every member except Nancy gave a speech. Ellen is not Nancy. Th erefore, Ellen gave a speech and Nancy sang a song. (Mx: x is a member; Sx: x sang a song; Gx: x gave a speech; e: Ellen;n: Nancy) Derive the conclusion of the following arguments. Use
6. Th e dog that bit the letter carrier is a large terrier. Ajax is a small dog. Th erefore, Ajax did not bite the letter carrier. (Dx: x is a dog; Bx: x bit the letter carrier;Lx: x is large; Tx: x is a terrier; a: Ajax) Derive the conclusion of the following arguments. Use conditional proof or
5. Th e author of King Lear was an English actor. John Milton was English but not an actor. Th erefore, John Milton is not the author of King Lear. (Wxy:x wrote y; Ex: x is English; Ax: x is an actor; k: King Lear; m: John Milton) Derive the conclusion of the following arguments. Use conditional
★4. The novel on the table was written by Margaret Mitchell. The only novel Margaret Mitchell wrote is Gone with the Wind. Th erefore, the novel on the table is Gone with the Wind. (Nx: x is a novel; Tx: x is on the table; Wxy: x wrote y; m: Margaret Mitchell; g: Gone with the Wind) Derive the
3. Th e artist who painted the Mona Lisa was a Florentine. Leonardo is the artist who painted the Mona Lisa. Th erefore, Leonardo was a Florentine. (Ax: x is an artist; Pxy: x painted y; Fx: x was a Florentine; m: the Mona Lisa; l: Leonardo) Derive the conclusion of the following arguments. Use
2. Ronald Reagan was the oldest U.S. president. Woodrow Wilson was a U.S.president. Woodrow Wilson is not Ronald Reagan. Th erefore, Ronald Reagan was older than Woodrow Wilson. (Ux: x is a U.S. president; Oxy: x is older than y; r: Ronald Reagan; w: Woodrow Wilson) Derive the conclusion of the
★1. Some of Jane Collier’s novels are interesting. Th e only novel Jane Collier wrote is Th e Cry. Th erefore, Th e Cry is interesting. (Nx: x is a novel; Wxy: x wrote y;Ix: x is interesting; j: Jane Collier; c: Th e Cry) Derive the conclusion of the following arguments. Use conditional proof
(20) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)[Fx ⊃ (Gx • x = n)]2. Gn ⊃ (∃x)(Hx • x =e) / Fm ⊃ He
(19) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(∃y)(Cxy ⊃ x = y)2. (∃x)(y)(Cxy • x =a) / Caa
(18) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)[Ex ⊃ (Hp • x = e)]2. (∃x)(Ex • x = p) / He
(17) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(Fx ⊃ x = e)2. (∃x)(Fx • x =a) / a = e
(16) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)[Nx ⊃ (Px • x = m)]2. ∼Pm / ∼Ne
(15) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(Rax ⊃ ∼Rxc)2. (x)Rxx / c ≠ a
(14) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (∃x)Gx ⊃ (∃x)(Kx • x = i) / Gn ⊃ Ki
(13) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(Ba ⊃ x ≠ a)2. Bc / a ≠ c
(12) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)[Rx ⊃ (Hx • x = m)] / Rc ⊃ Hm
(11) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(y)(Txy ⊃ x = e)2. (∃x)Txi / Tei
(10) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(Px ⊃ x = a)2. (x)(x = c ⊃ Qx)3. a = c / (x)(Px ⊃ Qx)
(9) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(Lx ⊃ x = e)2. (x)(Sx ⊃ x = i)3. (∃x)(Lx • Sx) / i = e
(8) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(x = r)2. Hr • Kn / Hn • Kr
(7) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(x = a)2. Fa / Fm • Fn
(6) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(Ax ⊃ Bx)2. Ac • ∼Bi / c ≠ i
(5) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(Gx ⊃ x = a)2. (∃x)(Gx • Hx) / Ha
★(4) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (∃x)(x = g)2. (x)(x = i) / g = i
(3) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(x = c ⊃ Nx) / Nc
(2) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. Ke 2. ∼Kn / e ≠ n
★(1) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(x = a)2. (∃x)Rx / Ra
★10. If there are any instructors, then if at least one classroom is available they will be eff ective. If there are either any textbooks or workbooks, there will be instructors and classrooms. Furthermore, if there are any classrooms, they will be available. Th erefore, if there are any
9. If anything is missing, then some person stole it. If anything is damaged, then some person broke it. Something is either missing or damaged. Therefore, some person either stole something or broke something. (Mx: x is missing; Px:x is a person; Sxy: x stole y; Dx: x is damaged; Bxy: x broke y)
8. If there are any policemen, then if there are any robbers, then they will arrest them. If any robbers are arrested by policemen, they will go to jail. Th ere are some policemen and Macky is a robber. Th erefore, Macky will go to jail. (Px: x is a policeman; Rx: x is a robber; Axy: x arrests y;
★7. Some people are friends of every person they know. Every person knows someone (or other). Th erefore, at least one person is a friend of someone. (Px: x is a person; Fxy: x is a friend of y; Kxy: x knows y) Translate the following arguments into symbolic form. Th en derive the conclusion of
6. Dr. Rogers can cure any person who cannot cure himself. Dr. Rogers is a person.Th erefore, Dr. Rogers can cure himself. (Px: x is a person; Cxy: x can cure y) Translate the following arguments into symbolic form. Th en derive the conclusion of each, using conditional proof or indirect proof when
5. If there are any honest politicians, then if all the ballots are counted they will be reelected. Some honest politicians will not be reelected. Th erefore, some ballots will not be counted. (Hx: x is honest; Px: x is a politician; Bx: x is a ballot;Cx: x is counted; Rx: x will be reelected)
★4. O’Brien is a person. Furthermore, O’Brien is smarter than any person in the class. Since no person is smarter than himself, it follows that O’Brien is not in the class. (Px: x is a person; Sxy: x is smarter than y; Cx: x is in the class) Translate the following arguments into symbolic
3. A horse is an animal. Th erefore, whoever owns a horse owns an animal. (Hx: x is a horse; Ax: x is an animal; Oxy: x owns y) Translate the following arguments into symbolic form. Th en derive the conclusion of each, using conditional proof or indirect proof when needed.
2. Whoever is a friend of either Michael or Paul will receive a gift . If Michael has any friends, then Eileen is one of them. Th erefore, if Ann is a friend of Michael, then Eileen will receive a gift . (Fxy: x is a friend of y; Rx: x will receive a gift ) Translate the following arguments into
★1. Any professional can outplay any amateur. Jones is a professional but he cannot outplay Meyers. Th erefore, Meyers is not an amateur. (Px: x is a professional;Ax: x is an amateur; Oxy: x can outplay y) Translate the following arguments into symbolic form. Th en derive the conclusion of each,
(20) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(y)[Axy ⊃ (Bx • Cy)]2. (x)(y)[(Bx ∨ Dy) ⊃ ∼Axy] / ∼(∃x)(∃y)Axy
(19) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (∃x)(y)Ayx ∨ (x)(y)Bxy 2. (∃x)(y)(Cy ⊃ ∼Byx) / (x)(∃y)(Cx ⊃ Axy)
(18) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)[Ax ⊃ (∃y)(By • Cxy)]2. (∃x)[Ax • (y)(By ⊃ Dxy)] / (∃x)(∃y)(Cxy • Dxy)
(17) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (∃x)(y)(Axy ⊃ Byx)2. (x)(∃y)(Byx ⊃ ∼Axy) / ∼(x)(y)Axy
(16)Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(Ax ⊃ Bx)2. (∃x)Bx ⊃ ∼(∃x)(∃y)Cxy / (∃x)Ax ⊃ ∼Cmn
(15) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (∃x)(y)(Ayx ⊃ ∼Axy) / ∼(x)Axx
(14) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x){Ax ⊃ [(∃y)(By • Cy) ⊃ Dx]}2. (x)(Bx ⊃ Cx) / (x)[Ax ⊃ (Bx ⊃ Dx)]
(13) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (∃x){Ax • (y)[(By ∨ Cy) ⊃ Dxy]}2. (∃x)Ax ⊃ (∃y)By / (∃x)(∃y)Dxy
(12) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (∃x)(y)[(Ay • By) ⊃ Cxy]2. (y)(Ay ⊃ By) / (y)[Ay ⊃ (∃x)Cxy]
(11) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (∃x){Ax • [(∃y)By ⊃ Cx]}2. (x)(Ax ⊃ Bx) / (∃x)Cx
(10) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(∃y)Axy ⊃ (x)(∃y)Bxy 2. (∃x)(y)∼Bxy / (∃x)(y)∼Axy
(9) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (∃x)(y)(Axy ⊃ Bxy)2. (x)(∃y)∼Bxy / ∼(x)(y)Axy
(8) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (∃x)[Ax • (y)(By ⊃ Cxy)]2. (x)(∃y)(Ax ⊃ By) / (∃x)(∃y)Cxy
(7) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (∃x)[Ax • (y)(Ay ⊃ Bxy)] / (∃x)Bxx
(6) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(y)(Ax ⊃ By)2. (∃x)(y)(Ay ⊃ Cx) / (x)(∃y)[Ax ⊃ (By • Cy)]
(5) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (∃x)Ax ⊃ (∃y)By / (∃y)(x)(Ax ⊃ By)
(4) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)(∃y)(Ax ⊃ By) / (x)Ax ⊃ (∃y)By
(3) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (∃x)[Ax • (y)(By ⊃ Cxy)]2. (∃x)Ax ⊃ Bj / (∃x)Cxj
(2) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)[Ax ⊃ (y)(By ⊃ Cxy)]2. Am • Bn / Cmn
★(1) Derive the conclusion of the following symbolized arguments. Use conditional proof or indirect proof as needed.1. (x)[Ax ⊃ (y)Bxy]2. Am / (y)Bmy
30. If there are any safe drivers, then some safe drivers will be hired. Translate the following statements into symbolic form.
29. If there are any safe drivers, then if none of the trucks break down they will be hired. (Sx: x is safe; Dx: x is a driver; Tx: x is a truck; Bx: x breaks down; Hx:x will be hired) Translate the following statements into symbolic form.
★28. All children in the fourth grade can read any of the books in the library. Translate the following statements into symbolic form.
27. Some children in the third grade can read any of the books in the library. (Cx:x is a child; Tx: x is in the third grade; Rxy: x can read y; Bx: x is a book; Lx: x is in the library) Translate the following statements into symbolic form.
26. Some lawyers will represent any person who will not represent himself. (Lx:x is a lawyer; Px: x is a person; Rxy: x represents y) Translate the following statements into symbolic form.
★25. Every lawyer will represent a wealthy client. (Lx: x is a lawyer; Rxy: x will represent y; Wx: x is wealthy; Cx: x is a client) Translate the following statements into symbolic form.
24. If there are any cheaters, then if all the referees are vigilant they will be punished.(Cx: x is a cheater; Rx: x is a referee; Vx: x is vigilant; Px: x will be punished) Translate the following statements into symbolic form.
23. If there are cheaters, then some cheaters will be punished. (Cx: x is a cheater;Px: x will be punished) Translate the following statements into symbolic form.
★22. Some policemen arrest every traffi c violator they see. (Px: x is a policeman;Axy: x arrests y; Tx: x is a traffi c violator; Sxy: x sees y) Translate the following statements into symbolic form.
21. Some policemen arrest only traffic violators. (Px: x is a policeman; Axy:x arrests y; Tx: x is a traffi c violator) Translate the following statements into symbolic form.
20. Some people admire every person they meet. Translate the following statements into symbolic form.
★19. Every person admires some people he or she meets. (Px: x is a person; Axy:x admires y; Mxy: x meets y) Translate the following statements into symbolic form.
18. Some people speak to whoever speaks to them. (Px: x is a person; Sxy:x speaks to y) Translate the following statements into symbolic form.
17. Some people break everything they touch. (Px: x is a person; Bxy: x breaks y;Txy: x touches y) Translate the following statements into symbolic form.
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