The number of elements of the power set of a set containing n elements is

Options

A. `2^(n-1)`
B. `2^(n)`
C. `2^(n)-1`
D. `2^(n+1)`

Explanation

To find 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**:
The power set of a set is defined as the set of all possible subsets of that set. This includes the empty set and the set itself.

2. **Number of Subsets**:
For any set with \( n \) elements, each element can either be included in a subset or not. Therefore, for each of the \( n \) elements, there are 2 choices (include the element or exclude it).

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:
\[ \text{Total subsets} = 2^n \]

4. **Conclusion**:
Hence, the number of elements in the power set of a set containing \( n \) elements is \( 2^n \).

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

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