Let be a family of sets and let B E . Prove that BC UAE A. Proof. Let E B. Define A = [Select] so that it guarantees that A € and also a EA. As we have chosen A particularly, * EA for [Select] AE. By definition of the union of family of sets, [Select] BCUAE A. V E UAE A. Hence

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.1: Sets And Geometry
Problem 12E: For the sets given in Exercise 9, is there a distributive relationship for intersection with respect...
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Let be a family of sets and let B E A. Prove that BCUAE A.
Proof. Let E B. Define A = [Select]
guarantees that A €
* EA for [Select]
of family of sets,
BCUAE A.
so that it
and also x EA. As we have chosen A particularly,
A E A. By definition of the union
[Select]
V
V
E UAE A. Hence
Transcribed Image Text:Let be a family of sets and let B E A. Prove that BCUAE A. Proof. Let E B. Define A = [Select] guarantees that A € * EA for [Select] of family of sets, BCUAE A. so that it and also x EA. As we have chosen A particularly, A E A. By definition of the union [Select] V V E UAE A. Hence
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