The problem asks us to find the power set of the set $A = \{a, b\}$. The power set of a set is the set of all possible subsets, including the empty set and the set itself.

1. Problem Description

The problem asks us to find the power set of the set $A = \{a, b\}$. The power set of a set is the set of all possible subsets, including the empty set and the set itself.

2. Solution Steps

The power set of a set $A$, denoted by $P(A)$, is the set of all subsets of $A$.

If a set $A$ has $n$ elements, then the power set $P(A)$ has $2^n$ elements. In our case, $A = \{a, b\}$, so $n = 2$. Therefore, $P(A)$ should have $2^2 = 4$ elements.

The subsets of $A = \{a, b\}$ are:

* The empty set: $\emptyset$

* The subsets with one element: $\{a\}$, $\{b\}$

* The subset with two elements: $\{a, b\}$

Therefore, the power set of $A = \{a, b\}$ is $P(A) = \{\emptyset, \{a\}, \{b\}, \{a, b\}\}$.

3. Final Answer

The power set of $A = \{a, b\}$ is $\{\emptyset, \{a\}, \{b\}, \{a, b\}\}$. Therefore, the correct answer is b.