Please see attached image... Let F be a collection of subsets of a set X. Then the intersection A of all o-algebras of subsets of X thatcontain F is a o-algebra that contains F. Moreover, it is the smallest o-algebra of subsets of X thatcontains F in the sense that any o-algebra that contains F also contains A.Solution:Let E represent the collection of all o-algebras of X that contain F as a subset. Meaning, FCB for allBe E. By hypothesis, A = N B.BeEShow that FCA.

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Answered: Let F be a collection of subsets of a…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 9E: In Exercises 610, a relation R is defined on the set Z of all integers, In each case, prove that R...

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Let F be a collection of subsets of a set X. Then the intersection A of all o-algebras of subsets of X that contain F is a o-algebra that contains F. Moreover, it is the smallest o-algebra of subsets of X that contains F in the sense that any o-algebra that contains F also contains A.