February 23, 2017

Homework Help: smallest algebra

Posted by sxxx123456 on Thursday, January 15, 2009 at 3:46pm.

Let F be a family of subsets of a set X such that empty set is the element of F. A subset A of X belongs to F1 if and only if either A is a subset of F or complement of A is the subset of F. A subset B of X belongs to F2 if and only if B is a finite intersection of sets in F1. A subset C of X belongs to F3 if and only if C is a finite union of sets in F2. Show that F3 is the smallest algebra which contains F.

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