X is a finite non empty set of n elements. The maximum number of ordered pairs ( $A, B$ ) of subsets

Question

X is a finite non empty set of n elements. The maximum number of ordered pairs ( $A, B$ ) of subsets of $X$ such that $\mathrm{A} \cap \mathrm{B}=\phi$ is

Professor PC Thomas Classes · Answer

Each element of X can be used to form set A or set B or can be rejected, i.e there are 3 choices for each element of X . So number of possibilities of forming $(\mathrm{A}, \mathrm{B})$ is $3^{\mathrm{n}}$.