This exercise asks you to show that a family A of subsets si

This exercise asks you to show that a family A of subsets similar to the previous exercise cannot occur in a finite set. Let S be a finite set, and let B be a non-empty family of subsets of S. Show that there must be beta elementof B such that no other member of B is a subset of beta.

Solution

Let S br finite.

Let B be a non-emepty family of subsets of S.

let a_i belongs to S, B={{a_i}{a_i,aj}.....}

there exist no {A} such that A is a subset of {a_i}.

which is contradiction.

==> S cannot be finite.