Question

1. Determine P(∅). 2. Determine P({1}). 3. Determine P({1, 2, 3}).  

Answer 1

1. $P(\empty)=\{\emptyset\}$
2. $P(\{1\})=\{\empty, \{ 1\}\}$
3. $P(\{1,2,3\})=\{\empty, \{1\}, \{2\}, \{3\}, \{1,2\}, \{1,3\}, \{2,3\}, \{1,2,3\} \}$

As a verification of these results we can check that we have $\#P(A)=2^{\# A}$.