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Prove that An (BUC) = (An B) U (An C).

Prove that An (BUC) = (An B) U (An C).

Advanced Engineering Mathematics
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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**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.
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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