How many elements are there in the reflexive relation defined on the set A = {1}?

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Solution

We know that any relation is a subset of the cartesian product. Before we find the reflexive relation, let's find the cartesian product. The cartesian product of A and A will have only one element (1,1). This is a necessary component of reflexive relation as 1 should be related to 1. Once we include this in our reflexive relation, there won't be any other element to add. So the reflexive relation will have only one element.

If we had more elements in the cartesian product, the number of elements in a reflexive relation will change based on which all elements we add to it apart from the essential elements like (1,1).

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