A set constant n elements. The power set of this set contains.

Options

A. ` n^(2) ` elements
B. ` 2^(lambda//2) ` elements
C. ` 2^(n ) ` elements
D. n elements

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, including the empty set and the set itself.

2. **Counting Subsets**:
- For any set with \( n \) elements, each element can either be included in a subset or not. This gives us two choices (include or exclude) for each element.

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**:
- Therefore, the power set of a set containing \( n \) elements contains \( 2^n \) subsets.

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

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