Let A={1,2,3}A = \{1, 2, 3\}A={1,2,3}. What is the power set P(A)\mathcal{P}(A)P(A)?
{∅,{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}\{\emptyset, \{1\}, \{2\}, \{3\}, \{1, 2\}, \{1, 3\}, \{2, 3\}, \{1, 2, 3\}\}{∅,{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
{{1},{2},{3},{1,2,3}}\{\{1\}, \{2\}, \{3\}, \{1, 2, 3\}\}{{1},{2},{3},{1,2,3}}
It has 23=82^3 = 823=8 elements.
It has 32=93^2 = 932=9 elements.