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Unformatted text preview: p1, p2, …, pn and the conclusion is q then (p1 ∧ p2 ∧ … ∧ pn ) → q is a tautology. ༉ Inference rules are “simple” argument forms that will be used to construct more “complex” argument forms. Rules of Inference for Proposi$onal Logic: Modus Ponens Corresponding Tautology: (p ∧ (p →q)) → q Example: Let p be “It is snowing.” Let q be “I will study discrete math.” “If it is snowing, then I will study discrete math.” “It is snowing.” “Therefore, I will study discrete math.” Modus Tollens Corresponding Tautology: (¬p ∧ (p →q)) → ¬q Example: Let p be “it is snowing.” Let q be “I will study discrete math.” “If it is snowing, then I will study discrete math.” “I will not study discrete math.” “Therefore, it is not snowing.” Hypothe$cal Syllogism Corresponding Tautology: ((p → q) ∧ (q → r)) → (p → r) Example: Let p be “it snows.” Let q be “I will study discrete math.” Let r be “I will get an A.” “If it snows, then I will study discrete math.” “If I study discrete math, then I will get an A.” “Therefore, If it snows, then I will get an A.” Disjunc$ve Syllogism Corresponding Tautology: (¬p ∧ (p ∨ q)) → q Example: Let p be “I will study discrete math.” Let q be “I will study physics.” “I will study discrete ma...
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This document was uploaded on 02/27/2014 for the course CS 215 at SIU Carbondale.
 Spring '14
 M.Nojoumian
 Computer Science

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