Asymmetric, Anti-Symmetric and Symmetric Relations
Difference between the asymmetric, anti-symmetric and symmetric relations
Asymmetric Relations |
Anti-Symmetric Relations |
Symmetric Relations |
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Relation R on a set A is said to be asymmetric if and only if (a, b) ∈ R, then (b, a) ∉ R, for all a, b ∈ A. |
Relation R on a set A is said to be antisymmetric, if aRb and bRa hold if and only if when a = b. |
Relation R is said to be symmetric iff, for elements a, b ∈ A, we have aRb, that is, (a, b) ∈ R, then we must have bRa, that is, (b, a) ∈ R. |
Example: a – b ≠ b – a |
Example:
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Example: a + b = b + a |
Symmetric Relations
Symmetric relation is a binary relation which satisfies that if aRb exists then bRa also exists for all a, b belongs to set S. If (a, b) belongs to R then (b, a) Also belongs to relation R. Example of symmetric relation includes “is equal to”, as if a = b is true then b = a is also true.
In this article, we will explore Symmetric relations, Symmetric relation definition, properties of Symmetric relations, and Symmetric Relations Examples. We will also solve some problems related to Symmetric relations. Let’s start our learning on the topic ” Symmetric Relation”.
Table of Content
- What is Relation in Math?
- Types of Relation
- What are Symmetric Relations?
- Symmetric Relation Definition
- Examples of Symmetric Relations
- Properties of Symmetric Relations
- Number of Symmetric Relations
- Symmetric Relation Formula
- How to Check Relation is Symmetric or Not?
- Asymmetric and Symmetric Relations
- Asymmetric, Anti-Symmetric and Symmetric Relations
- Symmetric Relations Examples
- Practices Question on Symmetric Questions