Define symmetric, asymmetric and antisymmetric relations.   

Ans:

Symmetric Relation

A relation R illustrated on a set A is said to be a symmetric relation if for any x, y ∈ A, if (x, y) ∈ R after that (y, x) ∈ R an instance of a symmetric relation is: 

Let A = {1, 2, 3} be a set and R be a relation on A illustrated as {(1, 2), (2, 1), (3, 1), (1, 3)} after that R is a symmetric relation.

Asymmetric Relation

A relation R on a set A is known as an asymmetric relation 

if (x, y) ∈ R ⇒ (y, x) ∉ R for x ≠ y

that is presence of pair (x, y) in R excludes the possibility of presence of (y, x) in R.   

Anti-Symmetric Relation

 A relation R on a set A is known an anti-symmetric relation if for x, y∈A

 (x, y) and (y, x) ∈ R ⇔ x = y

That is x ≠ y ⇒ either x ~R y or y ~R x or both.