Simplify using the Logical Equivalence Laws or Algebra of Propositions21. (~(P ^ S) v ~Q) ^ (P v ~Q) ^ ~(P ^S) Logical EquivalenceDouble negative law:-(~p) = pIdempotent laws:pap = ppvp = pCommutative laws:pvq = qvpdvb = 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^~qAbsorption laws:pv(pag) = ppa(pvq) = p

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Simplify using the Logical Equivalence Laws or Algebra of Propositions 21. (~(P ^ S) v ~Q) ^ (P v ~Q) ^ ~(P ^S)

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

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Simplify using the Logical Equivalence Laws or Algebra of Propositions

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

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