Question

Let X be any non-empty set containing n elements. Then what is the number of relations on X ?
A. `2^(n^(2))`
B. `2^(n)`
C. `2^(2n)`
D. `n^(2)`

Answer 1

Correct Answer - A
Number of elements in X, is n, then the number of relation on x means, number of elements of cartesian
product X `xx` X.
Since, n (X) = n.
So, `n(X xx X) = n.n`
then the total number of relations is `2^(n.n)=2^(n^(2))`