Use basic logical equivalences (see p. 13 of the lecture notes) to show that p → [(r ∧ (p ∨ q)) ∨ ((¬p ∧ ¬q) ∧ r)] is logically equivalent to ¬p ∨ r. Show all your work and write the names of the logical equivalences you are using at each step. Examples: Use basic logical equivalences to show thata) (p →g) (pv g)+(p+q) = + (zp vq) Implication Law((bv d) ^d) (q~~-P^-9bL V dz7 (pv (+p^q))یهㅅㄱup ^7 (2p^9) by De Morgan's Law=A(disjunctive version)1p ^ (7(7p) V79) by De Morgan's Law(conjunctive version)Double Negation~ (^p^p) V (zp^79) by DistributiveLaw (cory. version)311d₂^ (pV+q) by= (p^7p) v (ap^79) by commutativeLaw (canj. version)ته(bardz)с(contradiction)c V (7p179) by Complementarity(cong version)= (ap^79) Vc by comm. Law(dis. version)-p179 by IdentityLaw(disi. Version)

The logical equivalence between expressions plays a crucial role in simplifying complex statements.…

Answered: Use basic logical equivalences (see 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

Chapter1: Introduction

Section: Chapter Questions

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Use basic logical equivalences (see p. 13 of the lecture notes) to show that p → [(r ∧ (p ∨ q)) ∨ ((¬p ∧ ¬q) ∧ r)] is logically equivalent to ¬p ∨ r. Show all your work and write the names of the logical equivalences you are using at each step.

Examples: Use basic logical equivalences to show that
a) (p →g) (pv g)
+(p+q) = + (zp vq) Implication Law
((bv d) ^d) (q
~~-P^-9
bL V dz
7 (pv (+p^q))
یه
ㅅㄱ
up ^7 (2p^9) by De Morgan's Law
=
A
(disjunctive version)
1p ^ (7(7p) V79) by De Morgan's Law
(conjunctive version)
Double Negation
~ (^p^p) V (zp^79) by Distributive
Law (cory. version)
311
d₂
^ (pV+q) by
= (p^7p) v (ap^79) by commutative
Law (canj. version)
ته
(bardz)
с
(contradiction)
c V (7p179) by Complementarity
(cong version)
= (ap^79) Vc by comm. Law
(dis. version)
-p179 by Identity
Law
(disi. Version)

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