Which of the following formulas are logically equivalent to: (∀y)(P(x,y)→P(y,x))→P(x,x)? (No matter what the condition P means) (∀y)(P(y,y) --> P(y,y)) --> P(x,x) (∀z)(P(x,z) --> P(z,x)) --> P(x,x) (∀z)(P(x,z) --> P(z,x)) --> P(z,z) (∀x)(P(x,y) --> P(y,x)) --> P(x,x)
Which of the following formulas are logically equivalent to: (∀y)(P(x,y)→P(y,x))→P(x,x)? (No matter what the condition P means) (∀y)(P(y,y) --> P(y,y)) --> P(x,x) (∀z)(P(x,z) --> P(z,x)) --> P(x,x) (∀z)(P(x,z) --> P(z,x)) --> P(z,z) (∀x)(P(x,y) --> P(y,x)) --> P(x,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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Question
Which of the following formulas are logically equivalent to:
(∀y)(P(x,y)→P(y,x))→P(x,x)?
(No matter what the condition P means)
(∀y)(P(y,y) --> P(y,y)) --> P(x,x)
(∀z)(P(x,z) --> P(z,x)) --> P(x,x)
(∀z)(P(x,z) --> P(z,x)) --> P(z,z)
(∀x)(P(x,y) --> P(y,x)) --> P(x,x)
Expert Solution
Step 1 Solution
Formulas which is equivalent to the above expression will be
(b) (∀z)(P(x,z) --> P(z,x)) --> P(x,x)
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