Suppose $$A$$ is a finite set with $$n$$ elements. The number of elements in the Largest equivalence relation of $$A$$ is

The number of functions from an $$m$$ element set to an $$n$$ element set is

Let $${R_1}$$ and $${R_2}$$ be two equivalence relations on a set. Consider the following assertions:

(i)$$\,\,\,\,{R_1} \cup {R_2}$$ is an euivalence relation
(ii)$$\,\,\,\,{R_1} \cap {R_2}$$ is an equivalence relation

Which of the following is correct?

The number of equivalence relations on the set $$\left\{ {1,2,3,4} \right\}$$ is