1. **State the problem:** We are given a set $A = \{1, 2, 3\}$ and asked two questions about its power set $P(A)$. 2. **Number of elements in the power set:** The power set of a set $A$ is the set of all subsets of $A$. The number of elements in $P(A)$ is given by the formula: $$|P(A)| = 2^{|A|}$$ where $|A|$ is the number of elements in $A$. 3. **Calculate $|P(A)|$:** Since $|A| = 3$, we have: $$|P(A)| = 2^3 = 8$$ 4. **Identify the power set $P(A)$:** The power set includes all subsets of $A$, including the empty set and $A$ itself: $$P(A) = \{\emptyset, \{1\}, \{2\}, \{3\}, \{1, 2\}, \{1, 3\}, \{2, 3\}, \{1, 2, 3\}\}$$ 5. **Summary:** - The number of elements in the power set of $A$ is $8$. - The power set $P(A)$ is the set of all subsets listed above.