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The problem asks to define the **power set** of a given set.

### Definition of Power Set:
The power set of a set \( A \), denoted as \( \mathcal{P}(A) \), is the set of all possible subsets of \( A \), including the empty set and \( A \) itself. 

For example:
- If \( A = \{1, 2\} \), the power set \( \mathcal{P}(A) \) would be:
  \[
  \mathcal{P}(A) = \{\emptyset, \{1\}, \{2\}, \{1, 2\}\}
  \]

### General Properties:
- If a set has \( n \) elements, the power set contains \( 2^n \) elements, since each element can either be included or excluded from a subset.

Would you like more details on this concept or examples? Here are five questions related to this topic:

1. How do you calculate the number of subsets in a power set?
2. What is the power set of \( \{a, b, c\} \)?
3. How does the power set relate to set theory operations like unions and intersections?
4. How is the empty set represented in a power set?
5. Can a power set be infinite if the original set is infinite?

**Tip:** The power set of a finite set with \( n \) elements has \( 2^n \) subsets. Always remember to include the empty set!

Explore the definition and properties of the power set of a given set. Learn how to calculate the power set, which includes all possible subsets, and understand its relation to set theory. Suitable for students in Grades 9-12.

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