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Let

*F*and

*G*be σ-fields os subsets of

*S*.

(a) Let

*H*=

*F*intersection

*G*be the collection of subsets of

*S*lying in both

*F*and

*G*. Show that

*H*is a σ-field.

(b) Show that

*F*union

*G*, the collection of subsets of

*S*lying in either

*F*or

*G*, is not necessarilt a σ-field.