Philosophy

  (i.e., Part A–G). Total possible high score = 120 marks.PART A (15 QUESTIONS WORTH 2 MARKS EACH. TOTAL = 30 MARKS)Translate the followin" rel="nofollow">ing statements in" rel="nofollow">into symbolic form usin" rel="nofollow">ing upper case letters to represent affirmative ordin" rel="nofollow">inary language statements. Clearly in" rel="nofollow">indicate the simple statements you are symbolizin" rel="nofollow">ing and the symbol you are usin" rel="nofollow">ing to symbolize them.1. Tanzania becomes a bankin" rel="nofollow">ing centre given that Zanzibar attracts foreign capital.2. The crops will fail unless it rain" rel="nofollow">ins.3. Vancouver does not allow smokin" rel="nofollow">ing in" rel="nofollow">in restaurants.4. Bats are mammals only if they nourish their young with milk.5. Schultz knows nothin" rel="nofollow">ing if and only if Schultz gets a bribe.6. Roberto lacks wisdom.7. Neither birds nor snakes are mammals.8. If Walsh fails to win" rel="nofollow">in, then either Harper win" rel="nofollow">ins or Walsh and Harper are tied.9. If either David Beckham or Patrick Walsh attend the charity concert, then neither Britney Spears nor Christin" rel="nofollow">ina Aguilera will attend.10. Either Jodie Foster or Patrick Walsh wear black to the Grammys but it is not the case that both do.11. Ozone depletion in" rel="nofollow">in the atmosphere is a sufficient condition for in" rel="nofollow">increased cancer rates.12. A necessary condition for decreased crimin" rel="nofollow">inal activity is the legalization of cocain" rel="nofollow">ine.13. If evolutionary biology is correct, then higher life forms arose by chance, and if that is so, then it is not the case that there is any design in" rel="nofollow">in nature and divin" rel="nofollow">ine providence is a myth.14. If Alvin" rel="nofollow">in has a bill, then he is not a platypus if he has feathers.15. Given that Murphy is a bat only if he can fly, Murphy is not a bat.PART B (2 QUESTIONS WORTH 5 MARKS EACH. TOTAL = 10 MARKS)Symbolize the followin" rel="nofollow">ing arguments, usin" rel="nofollow">ing symbolized statements and the relevant truth–functional connectives. Indicate the upper case letters you use to symbolize ordin" rel="nofollow">inary language simple statements. Discern whether the argument is valid or in" rel="nofollow">invalid.1. Erik attain" rel="nofollow">ins Valhalla given that he is valiant. And Erik is depressed assumin" rel="nofollow">ing that he is not valiant. Furthermore, Erik fails to attain" rel="nofollow">in Valhalla only if he is not depressed. Thus, Erik is depressed.2. If the Gulf War was about oil and if human life is more valuable than oil, then the Gulf War was immoral. Human life is more valuable than oil, but the Gulf War was not about oil. Therefore, the Gulf War was not immoral.PART C (3 QUESTIONS WORTH 5 MARKS EACH. TOTAL = 15 MARKS)Provide truth tables to determin" rel="nofollow">ine whether the followin" rel="nofollow">ing symbolized statements are tautologous, self–contradictory, or contin" rel="nofollow">ingent. After completin" rel="nofollow">ing your truth table explain" rel="nofollow">in how it in" rel="nofollow">indicates your answer.1. (~Z • ~W) -> (Z ≡ W)2. [(G ⊃ (N ⊃ ~ G)] & [(N ≡ G) • (N v G)]3. B ⊃ [ ~ (A • B) ⊃ A]PART D (5 MARKS)Use the in" rel="nofollow">indirect method to determin" rel="nofollow">ine whether the followin" rel="nofollow">ing arguments are valid or in" rel="nofollow">invalid. If the argument is in" rel="nofollow">invalid in" rel="nofollow">indicate truth–values of the simple statements that demonstrates the in" rel="nofollow">invalidity.1. 1. H v ~ S2. H ⊃ Z3. ~ S ⊃ P4. Therefore, P ≡ ZPART E (5 MARKS)Use truth table to obtain" rel="nofollow">in an answer to the followin" rel="nofollow">ing question. Be sure to show your work. And explain" rel="nofollow">in how your truth table in" rel="nofollow">indicates your answer.Cin" rel="nofollow">indy, Jane and Amanda, witnessed a bank robbery. At trial, Cin" rel="nofollow">indy testified that Lefty did not enter the bank, and if Howard pulled a gun, then Conrad collected the money. Jane testified that if Howard did not pull a gun, then Lefty entered the bank. Amanda testified that if Conrad collected the money, then Howard pulled a gun. Is it possible that all three witnesses told the truth? If so, what can we conclude about Lefty, Howard, and Conrad?PART F (EACH QUESTION IS WORTH 5 MARKS. TOTAL = 35 MARKS)Answer each question as directly as possible. One paragraph should be adequate to answer each question.1. Upon in" rel="nofollow">inspection, we immediately note that the followin" rel="nofollow">ing argument is valid. Why is this so? Could this argument ever be sound?~A v ~BA • BTherefore, C 2. Recall the Addition rule of in" rel="nofollow">inference (ADD). Conventionally, it seems suspicious that a disjunction can be derived where one of the disjuncts could be any statement imagin" rel="nofollow">inable. Explain" rel="nofollow">in why ADD is a correct rule of in" rel="nofollow">inference.3. Consider the followin" rel="nofollow">ing derivation taken from a proof of validity.n. (A • B) v C                 ....n+1       A                n SIMPExplain" rel="nofollow">in why this derivation exhibits an in" rel="nofollow">incorrect use of the SIMP rule of in" rel="nofollow">inference. 4. Explain" rel="nofollow">in why the Conditional Proof (CP) is acceptable within" rel="nofollow">in our propositional logic natural deduction method.5. Explain" rel="nofollow">in why the Indirect Proof (IP) is acceptable within" rel="nofollow">in our propositional logic natural deduction method.6. Prove the followin" rel="nofollow">ing tautology usin" rel="nofollow">ing CP, IP, and any of the 18 rules of in" rel="nofollow">inference.[(A v B) • ~A] ⊃ B 7. Determin" rel="nofollow">ine whether the followin" rel="nofollow">ing pair of symbolized statements are logically equivalent. Provide a truth table to support your answer.(H • K) v (K v M)                      (~ H • ~ K) v (~ K • ~ M) PART G (EACH QUESTION IS WORTH 5 MARKS. TOTAL POINTS =20 MARKS)Provide a formal proof of validity of the followin" rel="nofollow">ing arguments usin" rel="nofollow">ing CP, IP, and any of the 18 rules of in" rel="nofollow">inference. Please note that I have changed the symbols used to represent conjunction and material conditional.1. 1. ~ A v ~ A2. A v B/∴ B 2. 1. (~J • K) ⊃ L2. ~ J/∴ ~ L ⊃ ~ K 3. 1. ~ R2. (R ⊃ S) ⊃ Q/∴ Q 4. 1. ~ (M ⊃ N)2. (M <-> K) ⊃ N3. K ⊃ M/∴ ~ (M ⊃ K)