ph126_2006_7_exam_answers

ph126_2006_7_exam_answers - PH126 Exam 20067 ANSWERS

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Unformatted text preview: PH126 Exam 20067 ANSWERS =========================================================== This is revision 2 Please email corrections to s.butterfill at warwick Revised versions will be posted as errors are corrected. References to proofs and rules in first order logic are to the system presented in Barwise & Etchemendy, Language, Proof & Logic. =========================================================== Q5. a) What is a logically valid argument? What does it mean to say that two sentences are logically equivalent? What is a logical truth? [10 Marks] See lecture handouts or the glossary of Language, Proof & Logic. Most candidates did poorly on this question; in particular, few could say clearly what a logical truth is. b) Prove the following arguments. Only the standard rules may be used. NB: Any correct proof will get full marks; the proofs here are only examples. i. Q P o Q [20 marks] ii. P Q P l Q P [20 marks] 1 iii. (P P) [20 marks] iv. P ( P R) [30 marks] 2 Q6 a) What is a connective? What is a truth functional connective? See lecture handouts or the glossary of Language, Proof & Logic. Most candidates did poorly on this question; in particular, few could say clearly what a truth functional connective is. [10 marks] b) Is It is possible that a truth functional connective? Explain your answer. [10 marks (1 for the correct answer, 9 for the explanation)] It is possible that is a connective. We can regard It is possible that as a one-place connective that forms a sentence when is replaced with a sentence. In order to be truth functional, the truth value of It is possible that would have to be determined by the truth value of the sentence replacing . But consider the following two sentences: 1. Two plus two is five....
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ph126_2006_7_exam_answers - PH126 Exam 20067 ANSWERS

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