Symmetric, Asymmetric and Antisymmetric
Symmetric: Symmetric Relation is a relation in which all x, y ∈ X, (x, y) ∈ R ⇒ (y, x) ∈ R
Asymmetric: Asymmetric Relation is a relation in which if for all x, y ∈ X, (x, y) ∈ R ⇒ (y, x) ∉ R
Antisymmetric: Antisymmetric Relation is a relation in which
- For all x, y ∈ X [(x, y) ∈ R and (y, x) ∈ R] ⇒ x = y
- For all x, y ∈ X [(x, y) ∈ R and x ≠ y] ⇒ (y, x) ∉ R
Asymmetric Relation
A relation is a subset of the cartesian product of a set with another set. A relation contains ordered pairs of elements of the set it is defined on. A relation is a subset of the cartesian product of a set with another set. A relation contains ordered pairs of elements of the set it is defined on.
Table of Content
- What is Relation in Maths?
- What is Asymmetric Relations?
- Properties of Asymmetric Relations
- Asymmetric and Symmetric Relations
- Examples of Asymmetric Relations
- Conclusion: Asymmetric Relation
- Sample Problems on Asymmetric Relations
- FAQs On Asymmetric Relation
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