# Relations And Functions For Class 12

The concepts of relation is used in relating two objects or quantities with each other.

Types of Relations-

A relation in set A is a subset of A x A. Thus, A x A are two extreme relations.

Empty Relation: If no element of A is related to any element of A, i.e. $R = \phi \subset A \times A$, then the relation in a set is called empty relation.

Universal Relation: If each element of A is related to every element of A, i.e. $R = A \times A$, then the relation is said to be universal relation.

A relation R in a set A is called-

Reflexive- if $(a,a) \in R$, for every $a \in A$.

Symmetric- if $(a_{1},a_{2}) \in R$ implies that $(a_{2},a_{1}) \in R$, for all $a_{1},a_{2} \in A$

Transitive- if $(a_{1},a_{2}) \in R$ and $(a_{2},a_{3}) \in R$ implies that $(a_{1},a_{3}) \in R$ for all $a_{1},a_{2}, a_{3} \in A$<

Equivalence Relation- A relation in a set A is equivalence relation if R is reflexive, symmetric and transitive.

#### Practise This Question

You are asked to construct a distance chart representing distances between cities given in a set with all the cities of the same set. What kind of matrix will come out of it?