exam 04 - Student number: The University of Hong Kong...

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Unformatted text preview: Student number: The University of Hong Kong Philosophy : PHIL 1006 Elementary Logic December 15, 2004 2.30 pm. — 3.30 pm. Answer ALL questions. Time allowed: 1 hour Write your answers on this exam paper. This paper has 6 pages in total. You may do rough work in the margins of the exam paper, or on the extra paper distributed to you. 1. For the following statements, write “T” if they are true or “F” if they are false, on the blanks in the answer box below. Explanation is not required. [20 marks] a. b. If some premises of an argument are false, then the argument is a valid one. If the conjunction of the premises of an argument is logically equivalent to its conclusion, then the argument is a valid one. The sentence “He likes light beer” involves a case of syntactic ambiguity, since we don’t know whether the word “light” is intended to describe the colour, taste, or calories of the beer. In a complex argument, one of the premises of a dilemma may be supported by a hypothetical syllogism. “Some Palestinians have complained that Suha Arafat has gained too much power, as she controls the flow of information about Arafat's condition and has taken charge of access to the ailing leader.” (Quoted from an article in Journalnow. com.) This passage presents a multi-reason argument. “We endorse the merger of the Kowloon-Canton Railway Corporation (KCRC) and the MTR Corporation Limited (MTRCL), owing to the following reasons: this may lead to a more effective utilization of resources and, in that case, we citizens can share the benefits of the merger exercise.” The argument presented in this passage has two co-premises. If (i) X and Y are inconsistent, and (ii) Y entails Z, then X may be logically equivalent to Z. If (i) X entails Y, but (ii) Y does not entail X, then both X and Y must be contingent. If “((P#Q)#Q)” entails “(~ (P#Q) v (P#Q))” (where “#” is a truth-functional connective), then “((P#Q)#Q)” is consistent. “Three people in this room have got scholarships. All scholarship holders are diligent. Therefore, there are some diligent people in this room.” The validity of this argument cannot be demonstrated in SL. N PHIL 1006 Final Dec. 04 2. Give counter-examples to the following arguments or statements. [15 marks] a. Either the air is clean or our health is endangered. The air is clean. Therefore, our health is not endangered. Answer: b. Mary is either studying or working in London. If she is studying in London, she can experience the European style of living. If she is working in London, she is used to the rainy season there. Therefore, she can experience the European style of living. Answer: c. If (i) X does not entail Y, but (ii) Y entails Z, then X entails Z. (Note: You are required to fill out two lines of their possible truth-values here, supposing that X, Y and Z are WFFs with only one sentence letter; and to fill out four lines in d and e, supposing that they each have two sentence letters.) d. If (i) X, Y and Z form an inconsistent set, (ii) X and Y are not logically equivalent to each other, (iii) Z is a tautology, and (iv) Z entails X, then X is contingent. Answer: e. If (i) X and Y are consistent with each other, (ii) Z is contingent, and (iii) Z entails X, then Z entails Y. Answer: PHIL 1006 Final Dec. 04 3 H ” ‘6 ’9 3. Logical equivalence: rewrite the following two WFFs using the symbols ~ , V , “(“ and “)” [6 marks]: a. (P & Q) Answer: 13- ((P& Q)-> Q) Answer: 4. Translate the sentences below into WFFs in SL using the following translation scheme [12 marks]: P: Our predictions were successful Q: Our theory was mistaken. R: Our deduction from the theory went wrong. S: Our experiment was flawed. T: We should reforrnulate our theory. U: We should reconsider our understanding of our theory. a. If our predictions were not successful, then if our theory was not mistaken, then either our deduction from the theory went wrong or our experiment was flawed. Answer: b. We should not reforrnulate our theory unless our theory was mistaken. Answer: c. Though our predictions were not successful, our theory was not mistaken. Answer: (1. We should reconsider our understanding of our theory, whenever our deduction from the theory went wrong. Answer: PHIL 1006 Final Dec. 04 4 5. Check whether the following sequent is valid or not by the indirect method [17 marks]: (A—->B),(C—>D),(~BV~C) l=(~Av~C) Indirect truth—table (including the order of steps): Is the argument valid? Yes No (Circle the correct answer.) 6. Let “@” be a truth-functional connective. It is known that “(P @ Q)” entails the following WFFs: (i) (P V Q) (ii) (P <-> Q) a. Give all the possible truth-tables of “(P @ Q)”. [15 marks] Answer (6a): b. Explain your answer to 6a. (Note: You may refer to some truth-table(s) if you prefer, and your explanation must not exceed 5 sentences.) Answer (6b): PHIL 1006 Final Dec. 04 5 7. Read the following argument map, which contains some errors. Redraw the map correctly in the answer box (on the next page). Write the numerals instead of sentences, except in the case of the hidden premise you suggest for representing the inference objection involved. Please write this sentence in the blank inside the box. You are not required to articulate other hidden premises. [15 marks] Key: C: Contention R: Reason 0: Objection IO: Inference objection [Abstracted and adapted from a passage in an article entitled “The Pros and Cons of Banking Online” by Karin Price Mueller.] C: [1] It is recommended to use Intemet-only banking. “ O: [6] Ifyour employer doesn't offer direct deposit -— electronically wiring [2] Intemet-only banks don’t have the expense of maintaining hundreds of local branches. [3] Their overall cost of doing business is lower than it is for their traditional counterparts. your paycheck to your bank -— you'll have to use snail mail to get money into your account. 0: [7] You'll be charged noncustomer fees by the banks whose ATMs you use. R: [4] They pass the savings on to consumers m-two IO: [9] Even mam ways: higher 7]} ' interest and lower fees. thoué’ you 11 be charged the noncustomer fee, the I nternet—only bank will give you R: [5] You'll have 24— your money back. hour access to your account, for free. R: [8] lntemet—only banks don't have their own ATM network PHIL 1006 Final Dec. 04 6 Answer: Hidden premise: [10] END OF PAPER ...
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exam 04 - Student number: The University of Hong Kong...

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