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We shall use the fact that the number of all subsets of -element set is
(a) Let By defenition, a biniry relation on a set is a subset of a Cartesian square Since , there are binary relations on the set
(b) Let us find the number of binary relations on the set that contain and . Since elements of a relation can be arbitrary elements of , the number of binary relation on that contain and is equal to the number of binary relations . Since , there are binary relations on the set that contain and .