Write down possible power set of Q = {{4,5} , {6,7},{8,9} }

The power set of a set \( Q \) is the set of all subsets of \( Q \), including the empty set and \( Q \) itself. Given \( Q = \{ \{4,5\}, \{6,7\}, \{8,9\} \} \), we can determine its power set by listing all possible combinations of the elements.

The power set of \( Q \) is:

\[
P(Q) = \{ \emptyset, \{\{4,5\}\}, \{\{6,7\}\}, \{\{8,9\}\}, \{\{4,5\}, \{6,7\}\}, \{\{4,5\}, \{8,9\}\}, \{\{6,7\}, \{8,9\}\}, \{\{4,5\}, \{6,7\}, \{8,9\}\} \}
\]

### Explanation:
- \( \emptyset \) is the empty set.
- The single-element subsets are: \( \{\{4,5\}\}, \{\{6,7\}\}, \{\{8,9\}\} \).
- The two-element subsets are: \( \{\{4,5\}, \{6,7\}\}, \{\{4,5\}, \{8,9\}\}, \{\{6,7\}, \{8,9\}\} \).
- The full set \( Q \) is also included: \( \{\{4,5\}, \{6,7\}, \{8,9\}\} \).

This power set has \( 2^3 = 8 \) elements, as expected for a set with three elements.

Do you have any questions or would you like more details on power sets?

Here are 5 related questions:
1. What is the power set of a set with 4 elements?
2. How does the power set of an empty set look?
3. How do power sets relate to set theory and logic?
4. Can you explain the difference between a subset and a proper subset?
5. How is the size of a power set determined?

**Tip:** The size of a power set of a set with \( n \) elements is always \( 2^n \).

Write down possible power set of Q = {{4,5}, {6,7}, {8,9}}

Discover how to find the power set of Q = {{4,5}, {6,7}, {8,9}}. This problem explains the concept of power sets in set theory, listing all possible subsets including the empty set. Suitable for students in Grades 8-10.

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