Question

If A is a finite set containing n distinct elements, then the number of relations on A is equal to ____________.

Options

• `2^n" ^2`

• 2 x 2

• 2n

• `"n"^2`

Answer 1

If A is a finite set containing n distinct elements, then the number of relations on A is equal to `underline(2^n" ^2)`.

Explanation:

n x n = n² is the number of items in A x A. As a result, the number of relations on A = the number of subsets of A x A = 2^{n x n} = `2^n" ^2`.