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Show that the family of regular languages is closed under finite union and intersection, that is, if $L_1,L_2,…, L_n$ are regular, then

           $L_U=\bigcup_{i=1,2,..,n}$$L_i$
and

           $L_I=\bigcap_{i=1,2,3,...,n}L_i$
are also regular.

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