In general if two finite sets contain exactly the same number of unique elements than the two sets are isomorphic to each other. Is this correct? An isomorphism => both 1-1 and onto. If two sets both have an equal number of unique elements than they must be onto because every element in one set is mappped to the other with none left. It is 1-1 because each unique element in one set maps to another unique element (that hasen't already been mapped).