The number of elements in the power set $$P(S)$$ of the set $$S = \left\{ {\left\{ \phi \right\},1,\left\{ {2,3} \right\}} \right\}$$ is

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

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

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