A logical equivalence is derived from Theorem 2.1.1. Supply a reason for each step. Theorem 2.1.1 Logical EquivalencesGiven any statement variables p, q, and r, a tautology t and a contradiction c, the following logical equivalenceshold.1. Commutative laws:P Vq = qVp(p V q) V r = p V (q V r)p V (q ^ r) = (p v q) ^ (p v r)P^q = q^p(p^q)^r=p ^ (q ^ r)рл (qvr) %3D(рлд)v(р^г)2. Associative laws:3. Distributive laws:4. Identity laws:p^t=pV c = pp5. Negation laws:PV ~p=tP^~p = c6. Double negative law:~(~p) = p7. Idempotent laws:p V p = pP^p=p8. Universal bound laws:Pvt=tрлс3Dс9. De Morgan's laws:~(p ^ q) = ~p V ~qp V (p ^ q) = P(p V q) = ~p^~qp^ (p v q) = p10. Absorption laws:11. Negations of t and c:~t = c~c = t (p v ~q) ^ (~p v~q)by (a)by (b)by (c)by (d)Therefore, (p V ~q) ^ (~p v ~q) = ~q.= (~qv p) ^ (~qv~p)~qV (p ^~p)ɔ ^ b~

Name: A logical equivalence is derived from Theorem 2.1.1. Supply a reason f
Uploaded: 2024-03-20T06:38:44.000Z
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Description: A logical equivalence is derived from Theorem 2.1.1. Supply a reason for each step. Theorem 2.1.1 Logical EquivalencesGiven any statement variables p, q, and r, a tautology t and a contradiction c, the following logical equivalenceshold.1. Commutativ