Prove that An (BUC) = (An B) U (An C).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need help with this foundations of mathematics homework problem.
![**Problem Statement**
Prove that:
\[ A \cap (B \cup C) = (A \cap B) \cup (A \cap C) \]
This is a demonstration of the distributive law in set theory. The goal is to show that the intersection of set \( A \) with the union of sets \( B \) and \( C \) is equivalent to the union of the intersections of set \( A \) with sets \( B \) and \( C \) individually.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b62c17d-5c05-48d6-ac2b-a3a7c31907f7%2F7cf0df3e-fbb5-4132-bfa0-ce72a5ef9223%2F4xp0hzm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement**
Prove that:
\[ A \cap (B \cup C) = (A \cap B) \cup (A \cap C) \]
This is a demonstration of the distributive law in set theory. The goal is to show that the intersection of set \( A \) with the union of sets \( B \) and \( C \) is equivalent to the union of the intersections of set \( A \) with sets \( B \) and \( C \) individually.
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