section_4.11_answers - PHIL12A Section answers, 11 April...

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Unformatted text preview: PHIL12A Section answers, 11 April 2011 Julian Jonker 1 How much do you know? 1. Translate the following pairs of sentences, and show by a chain of equivalences that they are equivalent: (a) i. It is not the case that all Ps are Qs. x(P(x) Q(x)) ii. Some Ps are not Qs. x(P(x) Q(x)) Proof of equivalence: x(P(x) Q(x)) x (P(x) Q(x)) equivalence for x (P(x) Q(x)) De Morgan x(P(x) Q(x)) Double negation (b) i. It is not the case that some Ps are Qs. x(P(x) Q(x)) ii. No Ps are Qs. x(P(x) Q(x)) Proof of equivalence: x(P(x) Q(x)) x (P(x) Q(x)) De Morgan x( P(x) Q(x)) De Morgan x(P(x) Q(x)) equivalence for 2. Which of the following sentences are logical truths? For each sentence, you should be able to explain why it is a logical truth, or produce a counterexample that shows that it is not. (a) (Ex 10.24) ( xCube(x) xDodec(x)) x(Cube(x) Dodec(x)) The direction of implication doesnt hold. Suppose half of the objects in the world are cubes and halfdirection of implication doesnt hold....
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section_4.11_answers - PHIL12A Section answers, 11 April...

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