LetIbe a nonempty set and for each $\displaystyle i\epsilon I $ let $\displaystyle X_{i} $ be a set.

Prove that if each $\displaystyle X_{i} $ is a subset of a given setS, then $\displaystyle e( \bigcup_{i\epsilon I} X_{i}) = \bigcap_{i\epsilon I} e X_{i} $

Please note thaterepresents the complement of a set.

Thank you as always!

Edit: Also note, of course, that we must show inclusion both ways.