∅ ⊂ A ∩B ⇔ A ⊃ ∅ ⊂ B ⇔ A ⊃ ⊂ B. Similarly, For U = universe, A ∪ B ⊂ U ⇔ A ⊂ U ⊃ B ⇔ A ⊂ ⊃ B. Now consider the set membership relation and its converse. Thus The opposite composition is the universal relation. The compositions are used to classify relations according to type: for a relation Q, when the identity relation on the range of Q contains QTQ, then Q is called univalent. When the identity relation on the domain of Q is contained in Q QT, then Q is called total. When Q is both univalent and total then it is a function. When QT is univalent, then Q is termed injective. When QT is total, Q is termed surjective. If Q is univalent, then QQT is an equivalence relation on the domain of Q, see Transitive relation#Related properties. See also References Binary relations Mathematical logic