Answered: Logic example question If I have (∀…

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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Logic example question If I have (∀ y)(P(y) → P(b)) Would an example of this being true be for all real numbers greater than 0 - y is evenly divisible by 9 and b is evenly divisible by 3 The false interpretation would be for P(b) to be true whether x is true or not. I cannot think of a domain and conditions where this could be true. I was hoping you could help me get unstuck.

Expert Solution

Step 1

The logical statement (∀ y)(P(y) → P(b)) means "for all y, if P(y) is true, then P(b) is true".

In your example, you are trying to show that this statement is true when y is a real number greater than 0 that is divisible by 9, and b is a number divisible by 3. This works as a valid example, because if P(y) is true (i.e., y is divisible by 9), then P(b) must also be true (i.e., b is divisible by 3).

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