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# section_4.25_answers - PHIL12A Section questions 25 April...

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PHIL12A Section questions, 25 April 2011 Julian Jonker 1 Formal proofs Decide whether the following arguments are valid or not. If they are, give formal proofs for them; otherwise give counterexamples. 1. (Ex 13.2) 1 x(Cube(x) Small(x)) 2 xCube(x) 3 xSmall(x) Proof: 1 x(Cube(x) Small(x)) 2 xCube(x) 3 a 4 Cube(a) Elim: 2 5 Cube(a) Small(a) Elim: 1 6 Small(a) Elim: 5, 4 7 xSmall(x) Intro: 3-6 1

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2. (Ex 13.3) 1 xCube(x) 2 xSmall(x) 3 x(Cube(x) Small(x)) Proof: 1 xCube(x) 2 xSmall(x) 3 e 4 Cube(e) Elim: 1 5 Small(e) Elim: 2 6 Cube(e) Small(e) Intro: 4, 5 7 x(Cube(x) Small(x) Intro: 3-6 3. (Ex 13.4) 1 ¬∀ xCube(x) 2 ¬∀ x(Cube(x) Small(x)) Proof: 1 ¬∀ xCube(x) 2 x(Cube(x) Small(x)) 3 a 4 Cube(a) Small(a) Intro: 2 5 Cube(a) Elim: 4 6 xCube(x) Intro: 3-5 7 Intro: 1, 6 8 ¬∀ x(Cube(x) Small(x)) ¬ Intro: 2-7 2
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section_4.25_answers - PHIL12A Section questions 25 April...

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