What is Asymmetric Relations?
An asymmetric relation is a specific type of binary relation on a set where the order of elements matters. In an asymmetric relation, if the pair (a, b) is in the relation, then the pair (b, a) must not be in the relation for any elements a and b from the set. In other words, the relationship is one-directional or asymmetric.
Asymmetric Relations Definition
A relation R on a set A is called asymmetric relation if
∀ a, b ∈ A, if (a, b) ∈ R then (b, a) ∉ R and vice versa,
where R is a subset of (A x A)
This if an ordered pair of elements “a” to “b” (aRb) is present in relation R then an ordered pair of elements “b” to “a” (bRa) should not be present in relation 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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