P(XUY
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))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed968904-deb1-4825-8d41-680832f6cf70%2F459011b2-fb5d-4134-a3b6-c4b127b4f3a8%2Fxh1uw5j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:P(X UY)S P(X) u P(Y))
Expert Solution
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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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