Let $$R$$ be a symmetric and transitive relation on a set $$A$$. Then

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

Let $$S$$ be an infinite set and $${S_1},\,\,{S_2},....\,\,{S_n}$$ be sets such that $${S_1} \cup {S_2} \cup ....... \cup {S_n} = S$$. Then

(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