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.
