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a logical equivalence is derived from Theo- rem 2.1.1. Supply a reason for each step. Theorem 2.1.1 Logical Equivalences Given any statement variables p, q,

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a logical equivalence is derived from Theo- rem 2.1.1. Supply a reason for each step. Theorem 2.1.1 Logical Equivalences Given any statement variables p, q, and r, a tautology t and a contradiction c, the following logical equivalences hold 1. Commutative laws 2. Associative laws 3. Distributive laws 4. Identity laws: 5. Negation laws 6. Double negative law 7. Idempotent laws 8. Universal bound laws:pv t t 9. De Morgan's laws 10. Absorption laws 11. Negations of t andc:~t PVPP ct by by (c) bv (d) Therefore, (p V -q) (~p v ~q)

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