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Verify the logical equivalences using the theorem below:

(p ∧ ( ~ ( ~ p ∨ q ) ) ) ∨ (p ∧ q) ≡ p

Theorem 2.1.1 Let p, q, and r be statement variables, t a tautology, and c a contradiction. The following logical equivalence

6. Double Negative: ~(~) =p 7. Idempotency: pAp=pi pvp =p 8. Universal Bounds: p V t =t; pac=c 9. De Morgans Laws: ~( p q) =

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(РЛ (~ (~Pv4) ) ) V Срл9) ЕР 3 (PN (AP) 1649)) v (19) {demorganlaw = (PA (РЛ~9)) V (РЛ 9) = ((РЛР) Л~4)) V (PA9) { Associativ

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