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Published byDerick Armstrong Modified over 9 years ago
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Quiz 5 1.5, 3.1 Methods of Proof.
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Quiz 5: Th. May 20 3.30-3.45 pm 1) Give 2 rules of inference and the tautologies on which they are based. 2) Explain what an indirect proof is and explain why it is a valid strategy to prove an implication of the form p q. 3) What is a vacuous proof? (explain). 4) Determine whether the following arguments are valid: a) “If x^2 is irrational then x is irrational”, ” the number x=1/3 is not irrational”, “therefore: the number x^2=(1/3)^2 is not irrational”. b) “Joe’s coat fits in his bag” “Joe’s bag fits in his car” “Therefore: Joe fits in his car”.
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Answers Quiz 5 1) Give 2 rules of inference and the tautologies on which they are based. - see book 2) Explain what an indirect proof is and explain why it is a valid strategy to prove an implication of the form p q. - you prove the equivalent propsoition: (NOT q) (NOT p) 3) What is a vacuous proof? (explain). - You prove p q by showing that p is always false, i.e. F q is always true. 4) Determine whether the following arguments are valid: a) “If x^2 is irrational then x is irrational”, ” the number x=1/3 is not irrational”, “therefore: the number x^2=(1/3)^2 is not irrational”. - yes valid: p q AND (NOT q) (NOT p). b) “Joe’s coat fits in his bag” “Joe’s bag fits in his car” “Therefore: Joe fits in his car”. -No not valid: one could conclude that Joe’s coat fits in his car, but not Joe itself.
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