# ph126_april_test_07-08_answers - UNIVERSITY OF WARWICK...

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Unformatted text preview: UNIVERSITY OF WARWICK April Test 2008 ANSWERS Revision 0.2 Please email mistakes to [email protected] PHILOSOPHY: Starting Logic (PH126) Time Allowed: 2 hours Candidates should answer ALL questions. Read carefully the instructions on the answer book and make sure that the particulars are entered on it. All questions carry equal weight. Candidates are reminded that their answers should be directed to the questions asked. Marks will not be awarded for irrelevant or tangential material. References to proofs and rules in first order logic are to the system presented in Barwise & Etchemendy, Language, Proof & Logic. Q1 a) Define ‘logically valid argument’. [ 5 m a r k s ] b) State the standard rules of proof for the following symbol: ¡ [5 marks] c) In each of the following proofs, there is an incorrect step. Identify the incorrect step and explain why it is incorrect. [5 marks each] i) 1. P ¡ (Q ¢ R) 2. Q ¢ Elim: 1 [Step 2 is incorrect. The rules of proof can only be applied to the connective with widest scope. In this case, ¢ Elim can only be applied to a conjunction, whereas the premise is a disjunction.] PH126T 1 ii) 1. P ¡ (Q ¢ R) 2. P 3. P ¡ Q ¡ Intro: 2 4. Q ¢ R 5. Q ¢ Elim: 4 6. P ¡ Q Reit: 3 7. P ¡ Q ¡ Elim: 1, 2-3, 4-7 [Step 6 is incorrect. Lines in a subproof cannot be cited after the subproof is closed. This is because closing a subproof means that the premises of that subproof are no longer assumptions.] d) Prove the following arguments. Only the standard rules may be used....
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