Logics for this lecture:

Relation \subseteq Cartesian Product
Relation on set A is defined as  R \subseteq A \times A
\phi and A \times A are two extreme subsets of   A \times A
If R = \phi , then relation is called empty relation.
If R = A \times A , then relation is called universal relation.
Both empty and universal relations are also known as trivial relations.