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Prove that each argumentation below is valid using Natural Deduction: 1. Vx. (T(x) v S(x)) -T (a) :. 3x. S(x) 2. Vx. (A(x) → (B(x) V C(x))) A(a) ^ ¬B(a) :. C (a) 3. Vx. (A(x) → Vy. (B(y) → C(x, y))) A(m) ^ B(n) :. C(m, n) 4. Vx. ((A(x) A B(x)) → C(x)) Vx. (A(x)→ C(x)) :-Vx. B(x) 5. 3x. A(x) → Vx. (B(x) → C(x)) 3x. D(x)→ 3x. -C(x) 3x. (A(x) ^ D (x)) :\x. B(x)

Prove that each argumentation below is valid using Natural Deduction: 1. Vx. (T(x) v S(x)) -T (a) :. 3x. S(x) 2. Vx. (A(x) → (B(x) V C(x))) A(a) ^ ¬B(a) :. C (a) 3. Vx. (A(x) → Vy. (B(y) → C(x, y))) A(m) ^ B(n) :. C(m, n) 4. Vx. ((A(x) A B(x)) → C(x)) Vx. (A(x)→ C(x)) :-Vx. B(x) 5. 3x. A(x) → Vx. (B(x) → C(x)) 3x. D(x)→ 3x. -C(x) 3x. (A(x) ^ D (x)) :\x. B(x)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 23E
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Prove that each argumentation below is valid using Natural Deduction: 1. Vx. (T(x) V S(x)) ¬T(a) : 3x. S(x) 2. Vx. (A(x) → (B(x) V C(x))) A(a) A¬B(a) : C(a) 3. Vx. (A(x) → Vy.(B(y) → C(x,y))) А(m) л В(п) : C(m,n) 4. Vx. ((A(x) ^ B(x)) → C(x)) Vx. (A(x) → C (x)) : Vx. B(x) 5. 3x. A(x) → Vx. (B(x) → C(x)) 3x. D(x) → 3x. –¬C(x) 3x. (A(x) A D(x)) : Vx. B(x)
Transcribed Image Text:Prove that each argumentation below is valid using Natural Deduction: 1. Vx. (T(x) V S(x)) ¬T(a) : 3x. S(x) 2. Vx. (A(x) → (B(x) V C(x))) A(a) A¬B(a) : C(a) 3. Vx. (A(x) → Vy.(B(y) → C(x,y))) А(m) л В(п) : C(m,n) 4. Vx. ((A(x) ^ B(x)) → C(x)) Vx. (A(x) → C (x)) : Vx. B(x) 5. 3x. A(x) → Vx. (B(x) → C(x)) 3x. D(x) → 3x. –¬C(x) 3x. (A(x) A D(x)) : Vx. B(x)
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