QUESTION 7 The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. Reference: Ref 8-1 1. (~ S v ~ R) ? ~ M 2. ~ S v ~ R 1, ___ A. Simp B. CD C. Conj D. Add QUESTION 8 The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. Reference: Ref 8-1 1. [(P ? R) ? S] ? [(Q ? R) ? T] 2. (P ? R) v (Q ? R) 3. S v T 1, 2, ___ A. Simp B. Add C. Conj D. CD QUESTION 9 The last line of each example gives the reference to the line or lines needed for its derivation. You are to determine the correct rule of inference. Reference: Ref 8-1 1. B v (S ? M) 2. ~ B 3. S ? M 1, 2, ___ A. DS B. MT C. HS D. MP
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Consider the following reduction ad absurdum proof in propositional logic. A combination of derivation lines (to the left, after the line numbers) and justification lines (to the right) are missing. Fill in the blanks. 1. (A v B) ⊃ (C . D) Premise 2. C ⊃ ~ D Premise/ Show ~ A 3. A Assumption for purposes of indirect proof 4. ___ 3, Add 5. C . D 1, 4, MP 6. C 5, Simp 7. ~ D ___ 8. D 8, Simp 9. D . ~ D 7, 8, Conj 10. A ⊃ (D . ~ D) 3– 9, Indirect Proof A v B; 2,6, MP; NC; ~ A A . B; 2,5 MP; DM, 9,10 MP A ⊃ B; 2,6 MP; 2 DN; ~ A A . B; 2,5 MP; NC; 9,10 DN
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One of the rules of inference is Disjunctive syllogism : Prove that Disjunctive syllogism is valid using the laws of propositional logic and any of the other rules of inference besides Disjunctive syllogism: (Hint: you will need one of the conditional identities from the laws of propositional logic):
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10. 7.3 III. Problem 1 Use the first thirteen rules of inference to derive the conclusion of the following symbolized argument. 1 (~M ⊃ P) • (~N ⊃ Q) 2 ~(M • N) / P v Q Add Line Use the following dropdown menus if you need help remembering the rules of inference. Rules of implication: Rules of replacement:
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