# What is Void or Empty Relation with Example ?

## Solution :

Let A be a set. Then, $$\phi$$ $$\subseteq$$ A $$\times$$ A and so it is a relation on A. This relation is called the void or empty relation on set A.

In other words, a relation R on a set A is called void or empty relation, if no element of A is related to any element of A.

Example : Consider the relation R on the set A = {1, 2, 3, 4, 5} defined by R = {(a, b) : a – b = 12}.

We observe that a – b $$\ne$$ 12 for any two elements of A.

$$\therefore$$   (a, b) $$\notin$$ R for any a, b $$\in$$ A.

$$\implies$$  R does not contain any element of A $$\times$$ A

$$\implies$$  R is empty set

$$\implies$$  R is the void relation on A.