ans1 - Problem Set 1 Elementary Logic Due 20 February 2008...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Problem Set 1 Elementary Logic Due: 20 February 2008 Name (W212 flgflfl gazed fig” (11$ l Student ID Number email Mark _____—% . Due 20 February 2007 by 4:00PM. Submit your problem set to Ms. Loletta Li in Main Building 312. Make sure your problem set is timestamped. Do not submit assignments by email. Late penalty: 10% for each day late. This problem set will not be accepted after 28 February. Answer the questions on the problem set itself. Write neatly. If the grader cannot read your handwriting, you will not receive credit. Be sure that all pages of the assignment are securely stapled together. Check the course bulletin board for announcements about the assignment. Do your own work. If you copy your problem set, or permit others to copy, you may fail the course. 1. (15 marks) True or false? Circle ‘T’ if the statement is true. Circle ‘F’ if the statement is false. For this question, you should assume that go is a WFF of SL. Every sound argument is a good argument. There is an SL WFF with truth-value both T and F. There is an expression of SL containing exactly 14 symbols. The premises and conclusion of a valid argument can all be false. No argument with a false conclusion contains a hidden assumption. If 90 contains the symbol “(” then‘tp contains a one-place connective. (p is not an expression of SL. The main connective of “~ ~ (~C&B)” is “85”. Logic describes how people reason. A lexically ambiguous word has more than one meaning in a language. No valid argument has a false conclusion. Whenever “(A ,4, B)” is true, “(A&B)” is also true. Some good arguments are JIlot valid arguments. “The pines of Rome” is a statement. The premises and conclusion of an invalid argument can all be true. /15 2. (5 marks) Which of the following is a valid argument? Circle “Yes” if it is a valid argument. Circle “No” if it is not a valid argument. Yes If Henry is cold, then Marge is cold. If Mary is cold, then Nero is cold. If Nero is cold, then Arnie is cold. So, if Henry is cold, then Arnie is cold. Yes If you feel thirsty, then drink tea. ‘ " You feel thirsty. So, drink tea. Yes Not all birds lay eggs. ' So, some birds lay eggs. Yes If it snows in Hong Kong, then it snows in Hong Kong. No Tokyo is in Japan. Tokyo is not in Japan. Nothing is both in Japan and not in Japan. Therefore, London is in France. 3. (15 marks) Make a correct truth table for each of the following WFFs of SL. @TTFF NFFTT @ FFFFV CTFTF NFTFT &FTFF MTTFF /15 th tables. Fill in the blanks with an SL WFF to make correct true 4. (15 marks) manta) MMRAJDM) (MW-t) v Iflzw‘flo v pm EEEHHEHEE ’U HEHEEHEHE HEEEEEHEE EHEEEEEHE ' HEEEHEEHI‘I EEEEHHEEM / 15 5. (5 marks) Is I“because” a truth~functi0nal connective? Using examples, explain why 01‘ why not. N0. Fflf/hJ/W 3 5 8 61/)ng 7w Aefazzm 3 RS d/Ir’fiyiée M/y éfl/erj/frgzw / :5 WM, uA/e 313a/MM2oiemse3234/aoddm Wg‘fl/se 4% 75077?" 0’ 8 A flu)” Me, 133 g/Mfi% 0% A” @7/W/ ”‘0’ 3’? woe/d W440 W W M (7%” WW; Km 16% [m 5 g/J/mfiflwimdgMgfgfldyfiWMf. - _, 7AM «54 Jami «11 “MW 5 7&74 ,3 a/irwfled ”1- UAW], M MM )9 mm) w waffle?» we fimd a 27m ””444 1%..) 6. (10 marks) Translate the following statements into SL. Preserve as much structure as possible. Use the following translation scheme: A: David is early. B: Mathilda is at home. C: Larry is nice. D: Lena is hungry. (a) If Lena is hungry, then Larry is nice if David is early. ( D ,9 (A ~95) ) (b) Whenever Lena is hungry and David is early, Larry is not nice. U D a A) ——7 we) (0) Mathilda is not at home, whether or not Larry is nice. (CC *9 ”B)£I(NC~=?¢B)) “wa9 “5) (d) Lena is hungry only if either Larry is nice or Mathilda is at home. (D~:?(Qvg)) / 10 7. (10 marks) Assume that each of the following three statements is true: If he likes chocolate, then he both thinks too much and eats too much. Either he likes chocolate and he thinks too much, or he does not like chocolate and he thinks too much and eats too much. He thinks too much. 1. Translate each of the three statements into SL, preserving as much structure as possible. Be sure to write down your translation scheme. L ‘ Millie; choc L —7 ( ,— (T‘g‘E)) T f m harms.» tam-lo ((Ler)v<~ramg)) g: Wank some». T 2. Does he like chocolate? /10 lt-‘7CT&EJ) ((larwlwflh‘tfléfl - T T TTT err res-Ho e (1%” [M M77124 FT T FETTTrr 8. (15 marks) For each, of the following: Circle “tautotogy” if it is a WFF of SL that is a tantology. Circle “contingent” if it is a contingent WFF of SL. Circle “inconsistent” if it is an inconsistent WFF of SL. Otherwise, don’t circle anything. ((A v ~13 ___, ~A) tautology ((A&(B&C)) .4 (A v 0)) contingent «A&oys(Av~A» tautology contingent (A ‘7'" (C +—+ A))&B) tautology Contingent _ (Mi .4 NBMflH on) tautology contin e _ (0' ——-> ((A&B) --+ (O V A))) /” """" ‘ @ contingent «AVBwionn~B» tautology ontingent (~ ~ A85 ~B -> 0)) tautoiogy tA-*(B—~+0))V((B~+C)W+A)) toutology T F \contin‘gent T ' l ((A H B) H ( .ALLLC H (A&C))) tautology ontingen inconsistent inconsistent inconsistent inconsistent inconsistent , inconsistent inconsistent inconsistent inconsistent inconsistent /15 9. (10 marks) Assume that each of the following four statements is false: If Andy does not play, then Andy and Stewart remember the song. Sting; does not sing. Either Andy plays and he remembers the song, or Andy does not play and Stewart does not remember the sang. Sting sings only if Stewart does not remember the song. 1. Translate each of the four statements into SL, preserving as much structure as possible. Be sure to write down your translation scheme. It] (NPHQX em) «:5 P Wrens - A./L}W17 1/1/me W3 ((PgA)\/(NP£<A’P)) RESJLWPWW SW3 (5 ”:2 fry/2) Sf Sting six/19$ (fl: {is (Mf 33 ;,,<:«_s ((PM)‘C§_‘T’ZE"’F’)___(LZ§:.) 1:137 ‘FT WP” PTFFPT 719,97 2. Does Andy play? No /10 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern