Let * be a binary operation on a nonempty set X and let Y be a nonempty subset of X and $\displaystyle \{ Z_i \} _{i \in I} $ be a family of nonempty subsets of X. Prove that:

$\displaystyle Y* \bigcup _{i \in I} Z_i = \bigcup _{i \in I } (Y*Z_i ) $