[Solved]Theorem Show S Follows Q R P P R R Q S Spoof 1 Q R P Given 2 Q R P Double Negation 1 3 Q Q37176844
Theorem: Show that s follows from (¬q ∨ r) → ¬p, ¬p → ¬r and r ∨(q ∧ s).
“Spoof”:
1. (¬q ∨ r) → ¬p Given
2. (¬q ∨ ¬¬r) → ¬p Double Negation: 1
3. ¬(q ∧ ¬r) → ¬p DeMorgan’s Law: 2
4. p → (q ∧ ¬r) Contrapositive: 3
5. p → ¬r ∧ Elim: 4
6. ¬p → ¬r Given
7. ¬r Proof by cases: 5, 6
8. r ∨ (q ∧ s) Given
9. q ∧ s ∨ Elim: 8, 7
10. s ∧ Elim: 9
(1) What is the most significant error in this proof? Give theline and briefly explain why it’s wrong.
(2) Show that the theorem is true. Do not need to repeat anyvalid arguments made in the original spoof.
Expert Answer
Answer to Theorem: Show that s follows from (¬q ∨ r) → ¬p, ¬p → ¬r and r ∨ (q ∧ s). “Spoof”: 1. (¬q ∨ r) → … . . .
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