Properties Reflexive Relation

In this class, We discuss Properties Reflexive Relation.

The reader should have prior knowledge of Introduction to Relations. Click here.

Reflexive relation:

A relation R on a set X is said to be reflexive if, for every x ∈ X, The ordered pair (x, x) present in relation.

Example:

X = {1, 2, 5}

R = {(1,1), (2,2), (5, 5), (2, 5)}

The above relation is reflexive because all the (x, x) pairs are present in the relation.

Example 2:

The relation “<=” on the set of real numbers.

The above relation is reflexive.

The set of real numbers is negative infinite to positive infinite.

Take any element from the real numbers set. We have x <= x.

The ordered pair (x, x) belongs to the relation.

Example 3:

The relation “<” on the set of real numbers is not reflexive.

Example 4:

The relation subset on the set of all subsets of a set

The above relation is reflexive.

X = {1, 2, 5}

{Φ, {1}, {2}, {5}, {1,2}, {1,5}, {2, 5}, {1, 2, 5}}

R = {(Φ, Φ), (1, 1), .. .}

All the elements satisfy x ⊆ x.