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The following proof uses the rules of inference to show that is a valid argument. (P₁) ((P₂) V P3), P2 → (P3) :. P₂ → P₁ →

The following proof uses the rules of inference to show that is a valid argument. (P₁) ((P₂) V P3), P2 → (P3) :. P₂ → P₁ →

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The following proof uses the rules of inference to show that is a valid argument. (¬P₁) → ((¬P₂) V P3), P2 → (P3) :. P₂ → P₁ 1. (¬P₁) → ((¬P₂) V P3) 2. P₂ → (¬P3) 3. P₂ 4. ¬P3 5. ¬P₁ 6. (¬P₂) V P3 7. ¬P₂ 8. P₂ ^ (P₂) 9. (P₁) (P₂^(-P₂)) 10. ¬(-P₁) 11. P₁ 12. P₂ → P₁ Write down the justifications for each of the twelve lines in the proof.
Transcribed Image Text:The following proof uses the rules of inference to show that is a valid argument. (¬P₁) → ((¬P₂) V P3), P2 → (P3) :. P₂ → P₁ 1. (¬P₁) → ((¬P₂) V P3) 2. P₂ → (¬P3) 3. P₂ 4. ¬P3 5. ¬P₁ 6. (¬P₂) V P3 7. ¬P₂ 8. P₂ ^ (P₂) 9. (P₁) (P₂^(-P₂)) 10. ¬(-P₁) 11. P₁ 12. P₂ → P₁ Write down the justifications for each of the twelve lines in the proof.
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