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Provide an interpretation that is true and one that is false: (∀ y)(P(y) → P(b))

Provide an interpretation that is true and one that is false: (∀ y)(P(y) → P(b))

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
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Provide an interpretation that is true and one that is false: (∀ y)(P(y) → P(b))
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Explanation

Let's first have a look at the logical meaning of the given statement.

We have the statement given as  (∀ y)(P(y) → P(b))  

Now from the above statement we can see that the we have ∀ in the statement which represents the all . Hence the statement becomes for all the y.

Then we have  P(y) → P(b)

Here the meaning is very very clear that is the property that hold true for the y should also hold true for the another element that is b .

Hence the complete logical meaning can be considered as the : For all the y, if P(y) is true, then P(b) is also true.

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