ph126_07-08_answers - PH126 Exam 20078 Answers = This is...

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PH126 Exam 2007–8 Answers =========================================================== This is revision 0.3. Please email corrections to s.butterfill@warwick.ac.uk PLEASE INCLUDE AT THE TOP OF THE PAPER References to proofs and rules in first order logic are to the system presented in Barwise & Etchemendy, Language, Proof & Logic. =========================================================== Q1 a) State the standard rules of proof for the following symbol: o [10 marks] b) What is a logically valid argument? What is a tautology? How are these two things related? [10 marks] c) Prove the following arguments. Only the standard rules may be used. [80 marks, 20 each] i) 10572d45-250e-4f38-9b79-3b3e08bff11d ± Q Q ² R R 9
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ii) 64c1ef73-402f-41a3-a538-f30f77a1fff9 (P ± (P oA )) oA iii) a8e6c5c0-1024-4d0a-b849-e5d0ec21b088 ² P o R P ³ R [ ] 2
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iv) [8ded8b46-b1d4-47df-b90b-bbdadd726de4] P Q l (Q l Q) (Q o R) ± (P o S) ² ( ² R ³² S) [ ] 3
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Q2 a) Use truth tables to establish whether the following arguments are valid. If any arguments are not valid, give counterexamples to them. If any arguments are valid, explain carefully why they are valid. [ 4 0 m a r k s , 1 0 e a c h ] i. e523597c-54a4-4e80-b0d5-10003d87c0a8 P ±² Q ² ( ² P ³ Q) [This argument is valid because there is no structure where the premise is true and the conclusion false] ii. 5bfef953-e1db-48cd-a11c-550f48827670 (P o Q) o P (P o R) o P [This argument is valid: there is no structure in which the premise is true and the conclusion false] 4
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iii. f6fae63f-ea73-413c-8a62-4218062aff4e (P o ± P) o ± (R o R) ± P ² (R l ± R) [This argument is not valid because in the first row of the truth table the
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ph126_07-08_answers - PH126 Exam 20078 Answers = This is...

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