set theory ,permutation and combination.

Question

Let P be the set of k elements.What is the number of ways we can choose an ordered pair (R,S).Where R and S are disjoint subsets of P.

Answer 1

For each element of $P$ there are $3$ choices: the element is in $R$, the element is in $S$ or the element is in neither. So ... there are $\color{red}{3^k}$ possibilities.