Simplify using the Logical Equivalence Laws or Algebra of Propositions. Do not simplify by indicating the binaries. 22. (~P -> (P -> Q)) -> (Q -> (P -> P))

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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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
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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