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Engineering
Computer Science
P(XUY

P(XUY

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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Question
P(X UY)S P(X) u P(Y))
Transcribed Image Text:P(X UY)S P(X) u P(Y))
Expert Solution
Step 1

Answer

P(X∪Y)⊆P(X)∪P(Y)

Now this statement is true if and only if X ⊆ Y or Y ⊆ A.

Suppose X ⊆ Y or X ⊆ Y

Without loss of generality, let’s assume X ⊆ Y

Suppose A ∈ P(X ∪ Y)

Suppose B ∈ A

Then B ∈ X or y ∈ Y

Since X ⊆ Y, B ∈ X implies B ∈ Y

Hence, B ∈ Y

So, B ∈ A implies B∈ Y, and hence A ⊆ Y

That is, A∈ P(Y), and so A ∈ P(X) ∪ P(Y)

Thus, we have shown that A ∈ P(X ∪ Y) implies A ∈ P(X) ∪ P(Y), and

so

P(X ∪ Y) ⊆ P(X) ∪ P(Y).

 

 

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