,
:which always holds (e.g. for ); hence is the universal relation on .

The compositions are used to classify relations according to type: for a relation Q, when the identity relation on the range of Q contains Q^TQ, then Q is called univalent. When the identity relation on the domain of Q is contained in QQ^T, then Q is called total. When Q is both univalent and total then it is a function. When Q^T is univalent, then Q is termed injective. When Q^T is