If the set A contains 5 elements, then the number of elements in the power set P(A) is equal to

Options

A. 32
B. 25
C. 16
D. 8

Explanation

To find the number of elements in the power set \( P(A) \) of a set \( A \) that contains 5 elements, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number of elements in the set \( A \)**:
Given that the set \( A \) contains 5 elements, we can denote this as:
\[ n = 5 \]

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:
\[ |P(A)| = 2^n \]
where \( n \) is the number of elements in the set \( A \).

3. **Substitute the value of \( n \)**:
Now, substituting \( n = 5 \) into the formula:
\[ |P(A)| = 2^5 \]

4. **Calculate \( 2^5 \)**:
We calculate \( 2^5 \):
\[ 2^5 = 32 \]

5. **Conclusion**:
Therefore, the number of elements in the power set \( P(A) \) is:
\[ |P(A)| = 32 \]

### Final Answer:
The number of elements in the power set \( P(A) \) is \( 32 \).

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