https://file.aiquickdraw.com/mathbot/file/17264998494922giduh0l.jpg

The question is asking to find \( n(A \cup B) \), which represents the number of elements in the union of sets \( A \) and \( B \). To solve this, we use the **union rule** in set theory, which is given by the formula:

\[
n(A \cup B) = n(A) + n(B) - n(A \cap B)
\]

We are provided with the following information:
- \( n(A) = 10 \)
- \( n(B) = 11 \)
- \( n(A \cap B) = 6 \)

Now, substituting these values into the union rule:

\[
n(A \cup B) = 10 + 11 - 6 = 15
\]

So, \( n(A \cup B) = 15 \).

Let me know if you need further clarification or details!

Here are 5 related questions to explore this topic further:
1. What is the difference between the union and the intersection of two sets?
2. How would the union rule change if \( A \) and \( B \) were mutually exclusive sets?
3. Can you explain the meaning of \( n(A \cap B) = 6 \) in the context of sets?
4. How does this problem change if we have three sets instead of two?
5. What is the general formula for the union of multiple sets?

**Tip**: The union rule is a key concept in set theory, and it's particularly useful when analyzing problems with overlapping groups or categories.

If n(A) = 10, n(B) = 11, and n(A ∩ B) = 6, what is n(A ∪ B)?

Learn how to use the union rule in set theory to calculate the union of two sets when given their intersection. This problem involves n(A) = 10, n(B) = 11, and n(A ∩ B) = 6, using the formula n(A ∪ B) = n(A) + n(B) - n(A ∩ B). Suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation