For each of the pairs of statements 1)-1v) below, do the appropriate one of the following: a) give an explanation why the two statements are logically equivalent; or b) give an explanation why one statement implies the other, and give a pair of predicates for p(x) and q(x) which shows that the two statements are not logically equivalent; or c) give two pairs of predicates for p(x) and g(x) which together show that neither state- ment implies the other. i) "-(p(x) and g(x))" and " p(x) and q(x)". ii) "(3x) (p(x) and g(x))" and "(3x) (p(x)) and (3 x) (g(x))". iii) (3x) (p(x) or q(x))" and "(Vx) (~p(x)) ⇒ (3x) (q(x))".
For each of the pairs of statements 1)-1v) below, do the appropriate one of the following: a) give an explanation why the two statements are logically equivalent; or b) give an explanation why one statement implies the other, and give a pair of predicates for p(x) and q(x) which shows that the two statements are not logically equivalent; or c) give two pairs of predicates for p(x) and g(x) which together show that neither state- ment implies the other. i) "-(p(x) and g(x))" and " p(x) and q(x)". ii) "(3x) (p(x) and g(x))" and "(3x) (p(x)) and (3 x) (g(x))". iii) (3x) (p(x) or q(x))" and "(Vx) (~p(x)) ⇒ (3x) (q(x))".
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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iv)
Transcribed Image Text:For each of the pairs of statements i)-iv) below, do the appropriate one of the following:
a) give an explanation why the two statements are logically equivalent; or
b) give an explanation why one statement implies the other, and give a pair of predicates
for p(x) and q(x) which shows that the two statements are not logically equivalent; or
c) give two pairs of predicates for p(x) and q(x) which together show that neither state-
ment implies the other.
i) "-(p(x) and q(x))" and "-p(x) and -q(x)".
ii) "(3x) (p(x) and g(x))" and "(3x) (p(x)) and (3 x) (g(x))".
iii) "(x) (p(x) or q(x))" and "(V x) (~p(x)) ⇒ (3 x) (q(x))”.
iv) "(Vx) (3 y) (p(x, y))" and "(3 y) (V x) (p(x, y))".
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