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Unformatted text preview: Will be done in class. 5 Proof of Logical Equivalence by Derivation (These use the Table of Logical Equivalences (6,7,8 [5,6,7 in ed.5]) in Section 1.2 plus other known Equivalences as "reasons" for steps in the proof. See Examples 6 and 7 (5 and 6 in ed. 5) for further illustrations) Prove: p > p\/q is a tautology: 1. p> p\/q Starting point 2. p \/ (p\/q) Implication law (Tbl 6[5 ed. 5]) 3. (p\/p) \/ q Associative laws 4. T \/ qp\/p is a known tautology 5. T Identity laws QED Prove p<>q <=> p<>q: 1. p<>q Starting point 2. (p>q) /\ (q>p) Proven in class 3. (q>p) /\ (p>q) Contrapositive Law 4. (q>p) /\ (p>q) Double Negation Law 5. (p>q) /\ (q>p) Commutative Laws 6. p<>q Same reason as in 2. 6...
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 Spring '08
 WATKINS
 Logic, p\/q

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