Question

If A is a finite set consisting of n elements, then the number of reflexive relations on A is

Options

• `2^(1/2(n^2 - n))`

• `2^(1/2(n^2 + n))`

• `2^(n^2 - n)`

• `2^(n^2 + n)`

Answer 1

`2^(n^2 - n)`

Explanation:

Given that n(A) = n

∴ n(A × B) = n × n = n²

Number of order pair = n²

A relation is called reflexive if (a, a) ∈ R.

There are n ordered pairs of the form (a, a), so there are n² – n ordered pair for a reflexive relation.

Hence, the total number of reflexive relations is `2^(n^2 - n)`.