If `A={a,{b}}`, then P(A) equals.

Options

A. `{phi,{a},{{b}},{a,{b}}}`
B. `{phi,{a}}`
C. `{{a},{b},phi}`
D. `{{b},{a,b}}`

Answer

To find the power set of the set \( A = \{ a, \{ b \} \} \), we will follow these steps:

### Step 1: Identify the elements of set \( A \)
The set \( A \) contains two elements:
1. \( a \)
2. \( \{ b \} \)

### Step 2: Determine the subsets of set \( A \)
The subsets of a set can be found by considering all combinations of its elements, including the empty set. For the set \( A \), the subsets are:
1. The empty set: \( \emptyset \)
2. The subset containing the first element: \( \{ a \} \)
3. The subset containing the second element: \( \{ \{ b \} \} \)
4. The subset containing both elements: \( \{ a, \{ b \} \} \)

### Step 3: List all subsets to form the power set
The power set \( P(A) \) is the set of all subsets of \( A \). Therefore, we can write:
\[ P(A) = \{ \emptyset, \{ a \}, \{ \{ b \} \}, \{ a, \{ b \} \} \} \]

### Final Answer
Thus, the power set \( P(A) \) is:
\[ P(A) = \{ \emptyset, \{ a \}, \{ \{ b \} \}, \{ a, \{ b \} \} \} \]