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EXERCISE 1.12.3: Proving the rules of inference using other rules. Some of the rules of inference can be proven using the other rules of inference and the laws of propositional logic. (a) One of the rules of inference is Modus tollens: P→q -q A-P Prove that Modus tollens is valid using the laws of propositional logic and any of the other rules of inference besides Modus tollens. (Hint: you will need one of the conditional identities from the laws of propositional logic). (b) One of the rules of inference is Modus ponens: P→q P q Prove that Modus ponens is valid using the laws of propositional logic and any of the other rules of inference besides Modus ponens. (Hint: you will need one of the conditional identities from the laws of propositional logic). (c) One of the rules of inference is Disjunctive syllogism: pvq -P q 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).

EXERCISE 1.12.3: Proving the rules of inference using other rules. Some of the rules of inference can be proven using the other rules of inference and the laws of propositional logic. (a) One of the rules of inference is Modus tollens: P→q -q A-P Prove that Modus tollens is valid using the laws of propositional logic and any of the other rules of inference besides Modus tollens. (Hint: you will need one of the conditional identities from the laws of propositional logic). (b) One of the rules of inference is Modus ponens: P→q P q Prove that Modus ponens is valid using the laws of propositional logic and any of the other rules of inference besides Modus ponens. (Hint: you will need one of the conditional identities from the laws of propositional logic). (c) One of the rules of inference is Disjunctive syllogism: pvq -P q 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).

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...
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EXERCISE 1.12.3: Proving the rules of inference using other rules. Some of the rules of inference can be proven using the other rules of inference and the laws of propositional logic. (a) One of the rules of inference is Modus tollens: P→q -q A-P Prove that Modus tollens is valid using the laws of propositional logic and any of the other rules of inference besides Modus tollens. (Hint: you will need one of the conditional identities from the laws of propositional logic). (b) One of the rules of inference is Modus ponens: P→q P q Prove that Modus ponens is valid using the laws of propositional logic and any of the other rules of inference besides Modus ponens. (Hint: you will need one of the conditional identities from the laws of propositional logic). (c) One of the rules of inference is Disjunctive syllogism: pvq -P q 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). (d) One of the rules of inference is Resolution: pvq -pvr Aqvr Prove that Resolution is valid using the laws of propositional logic and any of the other rules of inference besides Resolution. (Hint: you will need one of the conditional identities from the laws of propositional logic). Feedback?
Transcribed Image Text:EXERCISE 1.12.3: Proving the rules of inference using other rules. Some of the rules of inference can be proven using the other rules of inference and the laws of propositional logic. (a) One of the rules of inference is Modus tollens: P→q -q A-P Prove that Modus tollens is valid using the laws of propositional logic and any of the other rules of inference besides Modus tollens. (Hint: you will need one of the conditional identities from the laws of propositional logic). (b) One of the rules of inference is Modus ponens: P→q P q Prove that Modus ponens is valid using the laws of propositional logic and any of the other rules of inference besides Modus ponens. (Hint: you will need one of the conditional identities from the laws of propositional logic). (c) One of the rules of inference is Disjunctive syllogism: pvq -P q 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). (d) One of the rules of inference is Resolution: pvq -pvr Aqvr Prove that Resolution is valid using the laws of propositional logic and any of the other rules of inference besides Resolution. (Hint: you will need one of the conditional identities from the laws of propositional logic). Feedback?
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