Determine whether ∀x(P (x) ↔ Q(x)) and ∀x P (x) ↔∀xQ(x) are logically equivalent. Justify your answer 44. Determine whether Vx(P(x) → Q(x)) and Vx P(x) →VxQ(x) are logically equivalent. Justify your answer.

Answered: Determine whether Vx (P(x) → Q(x)) and…

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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Determine whether ∀x(P (x) ↔ Q(x)) and ∀x P (x) ↔
∀xQ(x) are logically equivalent. Justify your answer

44. Determine whether Vx(P(x) → Q(x)) and Vx P(x) →
VxQ(x) are logically equivalent. Justify your answer.

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Introduction:

In first-order logic, logical equivalence is a relationship between two statements that hold true under the same interpretation of the variables. If two statements are logically equivalent, then they are interchangeable and have the same truth value. In this problem, we are given two statements, and we need to determine whether they are logically equivalent.

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