Find Power set of the set `A={phi,{phi}}`.

Answer

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

### Step 1: Understand the Set
The set \( A \) contains two elements:
1. The empty set \( \phi \)
2. The set containing the empty set \( \{\phi\} \)

### Step 2: Determine the Number of Subsets
The power set of a set with \( n \) elements contains \( 2^n \) subsets. Here, the set \( A \) has 2 elements, so:
\[ n = 2 \implies 2^n = 2^2 = 4 \]
Thus, the power set will have 4 subsets.

### Step 3: List All Possible Subsets
The subsets of the set \( A \) can be formed by including or excluding each element. The subsets are:
1. The empty set \( \phi \)
2. The set containing only the first element \( \{\phi\} \)
3. The set containing only the second element \( \{\{\phi\}\} \)
4. The set containing both elements \( \{\phi, \{\phi\}\} \)

### Step 4: Write the Power Set
Now, we can write the power set \( P(A) \):
\[ P(A) = \{\phi, \{\phi\}, \{\{\phi\}\}, \{\phi, \{\phi\}\}\} \]

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

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