Void Relation, Universal Relation, Identity Relation

If  A  and  B  are two sets then a relation  R  from   A to B   is a sub-set of   A × B  .
If      (i)   R = Φ , R  is called a Void relation.
         (ii)  R = A × B  , R  is called a Universal relation.
         (iii) If  R  is a relation defined from  A to A , it is called a relation defined on  A .
         (iv)  R = { (a,a)  ∀  a ∈ A } , is called the identity relation.