A set contains n elements. The power set contains

Options

A. n elemets
B. `2^(n)` elements
C. `n^(2)` elemets
D. none of these

Answer

To solve the problem of finding the number of elements in the power set of a set containing \( n \) elements, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Power Set**:
- A power set is the set of all possible subsets of a given set. For a set \( A \) with \( n \) elements, the power set is denoted as \( P(A) \).

2. **Counting Subsets**:
- Each element in the set can either be included in a subset or not. Therefore, for each of the \( n \) elements, there are 2 choices (to include it or not).

3. **Calculating Total Subsets**:
- Since there are \( n \) elements and each can be included or excluded independently, the total number of subsets can be calculated using the formula:
\[ \text{Number of subsets} = 2^n \]

4. **Conclusion**:
- Thus, the number of elements in the power set \( P(A) \) is equal to the number of subsets of set \( A \), which is \( 2^n \).

### Final Answer:
The power set of a set containing \( n \) elements contains \( 2^n \) elements.

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