Relations

Given,
Since, is a relation on , therefore are the elements of . In the given options and satisfy the given relation, but in options and elements are not natural numbers.
Hence, option is the correct answer.

on set
Clearly, is symmetric and transitive.

Since the total number of possible relations from set A to B is 1024, each element in set A can be related to any of the elements in set B, i.e., each element in set A has n(B) possible choices for its image in set B.
Thus, the total number of possible relations from set A to B can be computed as the product of the number of choices for each element in set A, i.e.,

Given,