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.

Relations And Functions For Class 12

Relations And Functions For Class 12


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