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The question asks for the power set of the set \( \{0, 1, 2, 3, 4, 5, 6, 7\} \). 

### Power Set Definition:
The **power set** of a set \( S \) is the set of all subsets of \( S \), including the empty set and \( S \) itself. If a set has \( n \) elements, its power set will contain \( 2^n \) elements.

#### Given set:
\[ \{0, 1, 2, 3, 4, 5, 6, 7\} \]
This set contains 8 elements, so the power set will have:
\[ 2^8 = 256 \]
subsets.

Since listing all 256 subsets would be quite long, here are a few examples of subsets:
- Empty set: \( \emptyset \)
- Singletons: \( \{0\}, \{1\}, \{2\}, \{3\}, \{4\}, \{5\}, \{6\}, \{7\} \)
- Pairs: \( \{0, 1\}, \{0, 2\}, \{0, 3\}, \ldots \)
- Triples: \( \{0, 1, 2\}, \{0, 1, 3\}, \ldots \)
- And so on, until the full set itself: \( \{0, 1, 2, 3, 4, 5, 6, 7\} \)

Would you like further clarification or a deeper dive into specific types of subsets?

### Additional Questions:
1. What is the formula to calculate the number of subsets in a power set?
2. How does the size of the original set affect the size of its power set?
3. Can power sets be applied to sets with infinite elements?
4. What is the difference between a proper subset and a subset?
5. How would you list the power set of a smaller set, like \( \{1, 2, 3\} \)?

### Tip:
The power set is crucial in fields like logic and computer science, especially in dealing with possible states or combinations of conditions.

Write down power set of each of the following sets: {0, 1, 2, 3, 4, 5, 6, 7}

Explore how to write the power set of the set {0, 1, 2, 3, 4, 5, 6, 7}. Learn about subsets and how to calculate the number of subsets in any given set using the formula 2^n, where n is the number of elements in the set. Suitable for Grades 9-12.

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