Let $${\rm A}$$ be a finite set of size $$n$$. The number of elements in the power set of $${\rm A} \times {\rm A}$$ is

State whether the following statement are TRUE or FALSE:
(a) The union of two equivalence relations is also an equivalence relation.

(a) How many binary relations are there on a set A with n elements?

(b) How many one - to - one functions are there from a set A with n elements onto itself