Logical Equivalence - Todays Topics (11/4) I. Logically...

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3/4/11 Today’s Topics (11/4) I. Logically Equivalent Propositional Forms II. Logically Equivalent Propositions III. Two Rules of Equivalence a. Double Negation b. Contraposition IV. Equivalence and Validity
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3/4/11 I. Logically Equivalent Propositional Forms Two or more propositional forms are logically equivalent when there is no truth-value assignment on which they have different truth-values. Otherwise they are not logically equivalent.
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3/4/11 Example The following truth-table shows that the propositional forms ‘p’ and ‘p & p’ are logically equivalent. p p T T T F F F Since there is no row in which ‘p’ and ‘p &p’ have different truth- values, the two are logically equivalent
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3/4/11 Non-Equivalent Propositional Forms If there is at least one row in which two propositions have different truth- values, the propositional forms are p q p v q (p v q) T T T T T F T T F T T F F F F F Since there is at least one row in which ‘p v q’ and ‘(p v q) & p’ have different truth-values, they are NOT logically equivalent
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This note was uploaded on 03/03/2011 for the course PHIL 100 taught by Professor Forte during the Spring '08 term at Bridgewater State University.

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Logical Equivalence - Todays Topics (11/4) I. Logically...

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