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Given interpretations (a) (Vx) (y) P(x, y) → (3x)(Vy)P(x, y) (b) (Vx) [P(x) → Q(x)] → [(3x)P(x) → (Vx)Q(x)] (c) (Vx)[A(x)]' → [(Vx)A(x)]' to prove that each of the following wffs is not valid.

Given interpretations (a) (Vx) (y) P(x, y) → (3x)(Vy)P(x, y) (b) (Vx) [P(x) → Q(x)] → [(3x)P(x) → (Vx)Q(x)] (c) (Vx)[A(x)]' → [(Vx)A(x)]' to prove that each of the following wffs is not valid.

Database System Concepts
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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Given interpretations (a) (Vx) (y) P(x, y) → (x)(Vy) P(x, y) (b) (Vx) [P(x) → Q(x)] → [(x) P(x) → (Vx)Q(x)] (c) (Vx)[A(x)]' → [(Vx)A(x)]' to prove that each of the following wffs is not valid.
Transcribed Image Text:Given interpretations (a) (Vx) (y) P(x, y) → (x)(Vy) P(x, y) (b) (Vx) [P(x) → Q(x)] → [(x) P(x) → (Vx)Q(x)] (c) (Vx)[A(x)]' → [(Vx)A(x)]' to prove that each of the following wffs is not valid.
Expert Solution
Step 1

A. (∀x)( ∃y)P(x,y) → (∃x)( ∀y)P(x,y)

This wff is invalid because the quantifiers cannot be changed.

Suppose a property is true for some objects, then it is not necessary that the property holds for all objects.

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