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:...



Simplify using the Logical Equivalence Laws or Algebra of Propositions. Do not simplify by indicating the binaries.


22. (~P -> (P -> Q)) -> (Q -> (P -> P))




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

Extracted 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

Jun 02, 2022
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