Question

If set A contains 3 elements and the number of relations from set A to another set B is 64, find the number of elements in set B.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{elements}\mathrm{in}\mathrm{set}\mathrm{B}=\mathrm{x} \\ \mathrm{Then}, \\ {2}^{3\times \mathrm{x}}=64 \\ {2}^{3\mathrm{x}}=2^6 \\ 3\mathrm{x}=6 \\ \mathrm{x}=2 \\ \mathrm{So},\mathrm{number}\mathrm{of}\mathrm{elements}\mathrm{in}\mathrm{set}\mathrm{B}\mathrm{is}2. \end{gathered}$$