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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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