The power set (set of all subsets) of any given nonempty set forms a Boolean algebra, an algebra of sets, with the two operations (union) and (intersection). The smallest element 0 is the empty set and the largest element is the set itself.
the poWeR sET (sEt oF aLL subseTs) oF any GivEN nONEMpTy set forMs a boOleAn alGEbrA, aN alGebRa of sEts, wiTh The Two operaTions (union) and (inteRSectIon). The smALLesT eLemeNT 0 Is ThE EMPTy SEt and the LarGeSt elEmEnt is the sEt iTsELf.