Given n(A) = 1700,  n(A ∪ B) = 2250, and  n(A ∩ B) = 320, find n(B).

To find \( n(B) \), we can use the formula for the union of two sets \( A \) and \( B \):

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

Given:
- \( n(A) = 1700 \)
- \( n(A \cup B) = 2250 \)
- \( n(A \cap B) = 320 \)

We need to find \( n(B) \). Plugging in the values:

\[
2250 = 1700 + n(B) - 320
\]

Simplify the equation:

\[
2250 = 1380 + n(B)
\]

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

\[
n(B) = 2250 - 1380 = 870
\]

So, \( n(B) = 870 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the formula for the union of three sets?
2. How would you calculate \( n(A \cup B \cup C) \) if given \( n(A) \), \( n(B) \), \( n(C) \), and the intersections?
3. What does \( n(A \cap B) = 0 \) imply about the sets \( A \) and \( B \)?
4. How would you find \( n(A \cup B) \) if \( n(B) \) was unknown but \( n(A) \) and \( n(A \cap B) \) were given?
5. How can Venn diagrams be used to represent these set operations?

**Tip:** Always double-check your work by substituting your results back into the original equation to ensure accuracy.

Learn how to calculate n(B) using the given values of n(A), n(A ∪ B), and n(A ∩ B) through the principle of inclusion-exclusion. This step-by-step solution breaks down the key concepts in set theory and basic algebra. Suitable for students in Grades 8-10.

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