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Simplify using the Logical Equivalence Laws or Algebra of Propositions 24. S v ~(~P ^ ~Q) v ((P v Q) ^ S)

Simplify using the Logical Equivalence Laws or Algebra of Propositions 24. S v ~(~P ^ ~Q) v ((P v Q) ^ S)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Simplify using the Logical Equivalence Laws or Algebra of Propositions

24. S v ~(~P ^ ~Q) v ((P v Q) ^ S)

Logical Equivalence Double negative law: -(~p) = p Idempotent laws: pap = p pvp = p Commutative laws: pvq = qvp dvb = bvd |(p^q)ar = pA(qar) Associative laws: (ρvg)Vr v (qvr) Distributive laws: pa(qvr) = (p^q)v(par) pv (q a r) = (p v q) ^ (p v r) DeMorgan's laws: ~(paq) = ~pV~q ~(pvq) =~p^~q Absorption laws: pv(pag) = p pa(pvq) = p
Transcribed Image Text:Logical Equivalence Double negative law: -(~p) = p Idempotent laws: pap = p pvp = p Commutative laws: pvq = qvp dvb = bvd |(p^q)ar = pA(qar) Associative laws: (ρvg)Vr v (qvr) Distributive laws: pa(qvr) = (p^q)v(par) pv (q a r) = (p v q) ^ (p v r) DeMorgan's laws: ~(paq) = ~pV~q ~(pvq) =~p^~q Absorption laws: pv(pag) = p pa(pvq) = p
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