Use the Venn diagram to the right to determine the cardinality. 
n left parenthesis Upper A intersect Upper B right parenthesis
Upper Delta
U
A
B
$
%
two
four
eight
18
05
Question content area bottom
Part 1
n left parenthesis Upper A intersect Upper B right parenthesisequals
  
8

To solve this problem using the Venn diagram, we need to determine the cardinality of the intersection of sets $ A $ and $ B $, which is denoted as $ n(A \cap B) $.

Given:
- The problem asks for $ n(A \cap B) $.
- The value provided is $ 8 $.

Thus, the cardinality of the intersection of sets $ A $ and $ B $ is:

\[
n(A \cap B) = 8
\]

This means there are 8 elements that belong to both set $ A $ and set $ B $.

Would you like to dive deeper into this concept or have any further questions? Here are some related questions that might interest you:

1. What is the total number of elements in set $ A $ or set $ B $ combined?
2. How do you calculate the union of two sets using a Venn diagram?
3. What happens if $ n(A \cap B) $ is 0? What does that imply about the sets $ A $ and $ B $?
4. How can the principle of inclusion-exclusion be used to find the cardinality of the union of two sets?
5. What if the Venn diagram includes a third set $ C $? How does that change the calculation?

**Tip:** Remember, the intersection of sets represents elements that are common to all the sets involved. The Venn diagram is a great visual tool to understand relationships between different sets.

Learn how to determine the cardinality of the intersection of sets A and B using a Venn diagram. Given n(A ∩ B) = 8, understand the concept of set intersection and its application. Suitable for Grades 9-12 students studying set theory and cardinality.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation