The test is 105 minutes and its around 40 questions. I need an expert in Symbolic logic to understand what would be covered on the test and be prepared for it
B. Valid or invalid? Use the truth-assignment method to determine. Logic PHIL 2001 Elisabeta Sarca -----TEST 2 Name__________________________________________________________ Student Number____________________________________________ 1. Peonies are neither fragrant nor delicate, provided they are plastic. 2. To understand the material, it’s not sufficient to attend class. 3. You’ll reap the rewards of your work only if you have some luck and you persevere. 4. Flattering your teacher is neither necessary nor sufficient for getting a good grade. 5. Cats don’t cuddle unless they feel content and trust the person. 6. A necessary condition for my marrying you is that you buy me a Buick. 1. (T ⊃ (Y • S)) Y T 2. ((B• ~Z) v ~(~N v F)) (~K • F) ~(K v ~B) 3.((H • F) ⊃ R) ~R ~F 4. ~((Q v ~P) • ~W) ~(Q ⊃ ~A) ((A • ~C) • W) 1. Either you are lean and mean, or you are fluffy and jolly. Since you aren’t mean, you must be jolly. 2. To get to either London or Cardiff, you must take the train. You didn’t get to Cardiff, but you got to London. So, you must have taken the train. C. Translate into propositional logic and say whether valid or invalid. 2 points each x 6 = 12 points A. Translate into propositional wffs. 4 points each x 4 = 16 points 6 points each x 2 = 12 points ATTENTION: All responses (where applicable) should show clear evidence of the work through which you reached the answer. You may use the last page as scrap. Do not forget to write your name on the test! T = Y = S = B = Z = N = F = K = H = F = R = Q = P = W = A = C = 1. Unless the weather is inclement the match will take place, but our team will surely never give up. 2. Acing biology 101 is not a necessary condition for qualifying for medical school. 1. That Luna takes the express train is a sufficient condition for her getting to Hogwarts. Since she didn’t get to Hogwarts, it must be that she didn’t take the express train. 2. We’ll go to the picnic, unless we’ll play Twister. We won’t play both frisbee and Twister. So, we will go to the picnic, only if we’ll play frisbee. 1. (~D ~M) M ----------- ∴ 5. (~W ~Y) ~W ---------- ∴ 2. ~(L • ~S) ------------- ∴ 6. (~T v ~C) ------------ ∴ 3. ~(V ~N) ----------- ∴ 7. ~(X v ~U) ~X ---------- ∴ 4. ~(G • ~B) ~B ---------- ∴ 8. (~F ≡ J) ---------- ∴ E. Construct truth tables for the following arguments and determine whether valid or invalid. (You may use the short table method.) 5 points each x 2 = 10 points D. Construct truth tables for the following formulas. 3 points each x 2 = 6 points 1 point each x 8 = 8 points F. Which expressions can be derived? If nothing follows, write “nil”. 1. ((O v M) v ~(T ⊃ Y)) ~(O v M) ------------------------ ∴ 2. ~((A ⊃ ~B) v ~C) ------------------------ ∴ 3. ~((F ⊃ P) • Z) ~(F ⊃ P) ------------------------ ∴ 4. ((E • G) ≡ ~(H v L)) ------------------------ ∴ 1. ~((F v R) (S • T)) ~(F v ~S) ~T 2. ~((A v ~B) • (C D)) (E v X) (E A) (B ~X) ∴ C H. Say whether the following arguments are VALID (and give a PROOF) or INVALID (and give a REFUTATION). 5 points each x 2 = 10 points 3 points each x 4 = 12 points G. Derive everything that can be derived from the following premises. If nothing follows, write “nil”. 1. The party was zany, unless it wasn’t loud. Either the party was loud, or that the party was loud is not a necessary condition for it to be mad. That the party was zany is not a sufficient condition of its being quiet. [Z, L, M] 2. If you don’t get excellent results then you aren’t noticeable, unless you are intelligent. If you are adored, then you can’t both be intelligent and not get excellent results. ∴ You can’t both be adored and not get excellent results. [X, N, I, A] I. Translate the following arguments into symbols. Say whether VALID (and give a PROOF) or INVALID (and give a REFUTATION). 7 points each x 2 = 14 points Scrap paper, if needed. 17-Sep Syllogisms - Easier translations, star test, English Arguments, harder translations 1-19; 3rd 1-17 24-5ep | Syllogisms - Deriving conclusions, Venn diagrams, 2030;3rd1827 | HL: BF, EF, AEM, AET, BH, BS, idiomatic. Review BE 10ct | Test HZ: AHM, AHT, BD, BC, BI Propositional - Easier translations, simple truth-tables, equivalences, truth-evaluations, complex truth-tables 118-128; 3rd 112- 121 Propositional - truth-table test, truth-assignment test; harder translations, idiomatic arguments 129-142; 3rd 122- 135 H3: CEM, CET, DTE, DFE, DTH, DTM, DUE, DUM, DUH, DFM, DFH Proofs - Derivations: S-rules and I-rules. Easier and proofs and refutations 143-162; 3rd 136- 156 Ha: DAE, DAM, DAH, CHM, CHT, EI, ES, EE Proofs - Harder proofs and refutations. Review 167-175; 3rd 161- 170 HS: FSE, FSH, FIE, FIH, FCE, FCH, FTE, FTH, GEV, GE, GEC HE: GHV, GHI, GHC, GMC 19-Nov Quantificational - Easier translations 182-186; 3rd 182- 185 26-Nov Quantificational - Easier proofs and refutations 187-194; 3rd 186- 193 H7: HEM, HET 2Mer HR IFV IF IEC Sample Logic Quizzes Propositional Logic Sample Quiz Page 5 We’ll be able to have class, only if either there’s chalk in the room or else Gensler brought chalk. There’s no chalk in the room. So we won’t be able to have class. I say this, of course, because Gensler didn’t bring chalk. If Gensler is healthy and there’s snow, then Gensler is skiing. Gensler is healthy. Gensler isn’t skiing. Á There’s no snow. I’ll do poorly in logic. I’m sure of this because of the following facts. First, I don’t do LogiCola. Second, I don’t read the book. Third, I spend my time playing Tetris. As- suming that I spend my time playing Tetris and I don’t do LogiCola, then, of course, if I don’t read the book then I’ll do poorly in logic. If you either remain silent or tell the truth, then the mur- derer will know that your friend is hiding upstairs. You won’t tell the truth. Á The murderer won’t know that your friend is hiding upstairs. My tent will get wet and my food sack will get wet, assuming that it rains. My tent will get wet. So my food sack will also get wet. Either I will stay home and it will be sunny, or I will go backpacking and it will rain. I won’t go backpacking. Á It will be sunny. Translate into propositional logic and say whether valid or invalid. 6 points each Propositional Logic Sample Quiz Page 6 ((W Â F) Å ÀG) (C Ä (W Ã F)) G ÀW ÀF ÀF Á ÀW Á ÀC (W Ä (F Ã N)) ((W Â ÀF) Ä ÀN) ÀN N Á ÀW Á F ((S Ã L) Ä (P Â H)) ((D Â W) Ã (B Â M)) ÀS ÀD Á ÀP Á M À(U Â ÀJ) (ÀG Ä ÀL) À(Q Ã L) (ÀZ Ã J) (ÀZ Â ÀL) À(P Ä ÀZ) –––––––– ––––––––– –––––––– ––––––– –––––––– ––––––––– À(G Â H) (ÀH Ã ÀO) À(F Â ÀI) (O Ä ÀH) (U Ã ÀD) (ÀF Ä K) ÀG O ÀI H ÀD K ––––––– –––––––––– –––––––– –––––––– –––––––– –––––––– A is true only if B is true. If not either A or B, then C but not D. If A then B, or C. A or B, but not both. A is true, unless B and C are both true. Valid or invalid? 3 points each What letters (or negations of letters) follow? Leave blank if nothing follows. Translate into propositional logic wffs. 2 points each 2 points each Propositional Logic Sample Quiz Page 7 (ÀA Ä À(B Ã C)) (ÀA Ä (ÀB Ä C)) A ÀC Á ÀB (A Å (A Â B)) Á (A Ä B) Do a truth table for this formula. Test by the truth table method and say whether valid or invalid. 4 points 4 points each Propositional Logic Sample Quiz Page 8 A N S W E R S T O P A G E 5 1. (A¹ Ä (Rº Ã Gº)) ≠ 1 Valid ÀRº = 1 ÀGº = 1 Á ÀA¹ = 0 2. ((H¹ Â S¹) Ä Kº) ≠ 1 Valid H¹ = 1 ÀKº = 1 Á ÀS¹ = 0 3. ÀLº = 1 ÀWº = 1 T¹ = 1 ((T¹ Â ÀLº) Ä (ÀWº Ä Pº)) ≠ 1 Valid Á Pº = 0 4. ((S? Ã Tº) Ä K¹) = 1 Invalid ÀTº = 1 Á ÀK¹ = 0 5. (Rº Ä (T¹ Â Fº)) = 1 Invalid T¹ = 1 Á Fº = 0 We let R=0 to make the first premise true. 6. ((H? Â Sº) Ã (Bº Â R?)) ≠ 1 Valid ÀBº = 1 Á Sº = 0 A N S W E R S T O P A G E 6 1. ((W¹ Â Fº) Å ÀG¹) = 1 Invalid G¹ = 1 ÀFº = 1 Á ÀW¹ = 0 2. (C¹ Ä (Wº Ã Fº)) ≠ 1 Valid ÀWº = 1 ÀFº = 1 Á ÀC¹ = 0 3. (W¹ Ä (F¹ Ã Nº)) = 1 Invalid ÀNº =