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!