Let x and y be strings and let L be any language. We say that x and y are distin$-$ guishable 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 in L whenever yz in 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.