2. If n(A) = 200, n(B) = 100, and n(A ∪ B) = 250, what is n(A∩B)?

To find the number of elements in the intersection of two sets \( A \) and \( B \), denoted as \( n(A \cap B) \), we can use the formula related to the union and intersection of two sets:

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

Given:
- \( n(A) = 200 \)
- \( n(B) = 100 \)
- \( n(A \cup B) = 250 \)

Substitute these values into the formula:

\[
250 = 200 + 100 - n(A \cap B)
\]

Simplify the equation:

\[
250 = 300 - n(A \cap B)
\]

Now, solve for \( n(A \cap B) \):

\[
n(A \cap B) = 300 - 250
\]

\[
n(A \cap B) = 50
\]

So, the number of elements in the intersection of sets \( A \) and \( B \) is:

\[
\boxed{50}
\]

Would you like more details or have any questions?

### Related Questions
1. How would the result change if \( n(A \cup B) \) were 300?
2. Can \( n(A \cap B) \) ever be greater than \( n(A) \) or \( n(B) \)?
3. How do you calculate \( n(A - B) \) with the given information?
4. What is the general formula for \( n(A \cup B \cup C) \) for three sets?
5. How can Venn diagrams be used to visualize the union and intersection of sets?

**Tip:** Remember, the formula for the union of two sets is a helpful tool to find the intersection when you're given the individual set sizes and the size of their union.

Learn how to calculate the number of elements in the intersection of sets A and B using set theory principles. Given n(A) = 200, n(B) = 100, and n(A ∪ B) = 250, discover the formula for intersection and union of sets with a step-by-step solution.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation