Symmetric, Anti Symmetric and Asymmetric Relations on a set | 10 |

Symmetric, Anti Symmetric and Asymmetric Relations on a set | 10 |

In this lecture we will introduce the concept of Symmetric relations. We shall discuss how are symmetric relations different from Asymmetric and Anti-symmetric relations.

In discrete mathematics, a symmetric relation between two or more elements of a set is such that if the first element is related to the second element, then the second element is also related to the first element as defined by the relation. As the name 'symmetric relations' suggests, the relation between any two elements of the set is symmetric.
A relation R defined on a set A is said to be symmetric if, for elements a, b ∈ A, we have aRb, that is, (a, b) ∈ R, then we must have bRa, that is, (b, a) ∈ R. This implies that a relation defined on a set A is a symmetric relation if and only if it satisfies aRb ⇔ bRa for all elements a, b in A.

Learning Objectives:
1. Defining Symmetric relation on A
2. Defining anti-symmetric relation on A
3. Defining Asymmetric relation on A
4. Examples of each type
5. Difference between Symmetric, asymmetric and Anti-symmetric

This is useful for all those students who are preparing for any entrance that would test you on the basics of Advance mathematics and calculus, specifically

1. Basics for MA Economics
2. Semester Exam, mathematical methods
3. Indian Economic Services