If A={1,2,3} then the number of elements in P(A) is

Options

A. 6
B. 8
C. 12
D. 16

Answer

To find the number of elements in the power set \( P(A) \) of the set \( A = \{1, 2, 3\} \), we can follow these steps:

### Step 1: Identify the number of elements in set \( A \).
The set \( A \) contains the elements \( 1, 2, \) and \( 3 \). Therefore, the number of elements \( n \) in set \( A \) is:
\[ n = 3 \]

### Step 2: Use the formula for the number of elements in the power set.
The number of elements in the power set \( P(A) \) is given by the formula:
\[ \text{Number of elements in } P(A) = 2^n \]
Substituting the value of \( n \):
\[ \text{Number of elements in } P(A) = 2^3 \]

### Step 3: Calculate \( 2^3 \).
Now we calculate \( 2^3 \):
\[ 2^3 = 8 \]

### Conclusion:
Thus, the number of elements in the power set \( P(A) \) is \( 8 \).