Consider the first-order logic formula  ∃x (P(a, x) ˄ P(x, b)) and the interpretation  domain D = {Anna, Bob, Kelly}, P = {(Bob, Anna), (Anna, Kelly), (Bob, Bob), (Bob, Kelly), ((Kelly, Kelly)}, a = Anna, b =   Identify bound and free variables in the first-order logic formula ∀x A(x, y) ∧ ∀y B(x, y) Occurrence of x in A(x, y):      Occurrence of y in A(x, y):        Occurrence of x in B(x, y):        Occurrence of y in B(x, y):   Let x, y be variables whose domain is the set of real numbers ℝ. Which result of first-order logic justifies the statement below? ∀x∀y (x + y = 0) is logically equivalent to ∀y∀x (x + y = 0) Distributive laws Commutative laws Definability laws De Morgan’s laws

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
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Consider the first-order logic formula

 ∃x (P(a, x) ˄ P(x, b))

and the interpretation 

domain D = {Anna, Bob, Kelly}, P = {(Bob, Anna), (Anna, Kelly), (Bob, Bob), (Bob, Kelly), ((Kelly, Kelly)}, a = Anna, b =

 

Identify bound and free variables in the first-order logic formula

∀x A(x, y) ∧ ∀y B(x, y)

Occurrence of x in A(x, y):     

Occurrence of y in A(x, y):       

Occurrence of x in B(x, y):       

Occurrence of y in B(x, y):

 

Let x, y be variables whose domain is the set of real numbers ℝ. Which result of first-order logic justifies the statement below?

∀x∀y (x + y = 0) is logically equivalent to ∀y∀x (x + y = 0)


Distributive laws
Commutative laws
Definability laws
De Morgan’s laws
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