Let x and y be strings and let L be any language. We say that x and y are distinguishable by L if some string z exists whereby exactly one of the strings xz and yz is a member of L; otherwise, for every string z, we have xz 2 L whenever yz 2 L and we say that x and y are indistinguishable by L. If x and y are indistinguishable by L, we write x L y. Show that L is an equivalence relation.