What are the Types of Relations?
1.
Empty Relation
2.
Universal Relation
3.
Reflexive Relation
4.
Symmetric Relation
5.
Transitive Relation
1 1.
What is Empty Relation?
A Relation R in any set say A is said
to be Empty Relation if no elements of Set A is
related no elements of itself.
i.e. R
= ะค ⊃ A×A.
2. What is Universal Relation?
A Relation R in
any set say A is said to be Universal Relation if all elements of Set A is
related to its all elements.
i.e. R = A×A.
3. What is Reflexive Relation?
A Relation R in any set say A is said to be Reflexive Relation if
all same elements present in any Relation.
i.e. if (a, a) ∊ R, for every a ∈
A.
For Example R = {(1, 1), (2, 2), (a, a), (x, x)}
4.
What is Symmetric Relation?
A Relation R in any set say A is said to be
Symmetric Relation if all same elements present in any Relation R then its
mirror image also presents in that Relation.
i.e. if (a, b) ∊ R, then it implies (b,
a) ∊ R for all a, b ∈ A.
For Example R = {(1, 2), (2, 1), (a, b), (b, a), (x, y), (y, x)}
5. What is Transitive Relation?
A Relation R in any set say A is said to be Transitive
Relation
i.e. if (a, b) ∊ R, (b, c) ∊
R then it implies (a, c) ∊ R for all a, b, c ∈
A.
For Example R = {(1, 2), (2, 1), (1, 1), (b, a), (a, y),
(b, y)}
Note: Equivalence Relation:
A Relation R which is
Reflexive, Symmetric and Transitive said to be equivalence Relation.
