Question

please write summary and important points for relations and functions class 12​

Answer 1

Answer:

Empty Relation: It is the relation R in X given by R = .

Universal Relation: It is the relation R in X given by R = .

Reflexive Relation: A relation R in a set A is called reflexive if (a, a) ∈ R for every a ∈ A.

Symmetric Relation: A relation R in a set A is called symmetric if (, ) ∈ R implies that (, ) ∈ R, for all , ∈

Transitive Relation: A relation R in a set A is called transitive if (, ) ∈ R, and (, ) ∈ R together imply that all , , ∈ A.

EQUIVALENCE RELATION: A relation R in a set A is said to be an equivalence relation if R is reflexive, symmetric and transitive.

Equivalence Classes: Every arbitrary equivalence relation R in a set X divides X into mutually disjoint subsets (Ai) called partitions or subdivisions of X satisfying the following conditions:

All elements of Ai are related to each other for all i.

No element of Ai is related to any element of Aj whenever i ≠ j

· . These subsets () are called equivalence classes.