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The image contains the following problem related to set theory:

We are given the formula for the union of two sets:
\[
n(A \cup B) = n(A) + n(B) - n(A \cap B)
\]
### First Problem:
Given:
- \( n(A \cup B) = 20 \)
- \( n(A) = 12 \)
- \( n(A \cap B) = 5 \)

We need to find \( n(B) \).

Using the formula:
\[
20 = 12 + n(B) - 5
\]
Simplifying:
\[
20 = 7 + n(B)
\]
\[
n(B) = 13
\]

### Second Problem:
Given:
- \( n(A \cap B) = 3 \)
- \( n(B) = 5 \)
- \( n(A) = 6 \)
We need to find \( n(A \cup B) \).

Using the same formula:
\[
n(A \cup B) = n(A) + n(B) - n(A \cap B)
\]
\[
n(A \cup B) = 6 + 5 - 3 = 8
\]

Thus, the missing number is \( n(A \cup B) = 8 \).

Would you like any further details on this? Here are some related questions to expand on:

1. What happens when \( A \) and \( B \) are disjoint sets?
2. How can we visualize this with Venn diagrams?
3. What is the general formula for the union of three sets?
4. How can we apply this formula to probability problems?
5. How does this relate to the inclusion-exclusion principle?

**Tip:** When solving set problems, drawing Venn diagrams can help in visualizing intersections and unions effectively!

Explore the equation for finding the number of elements in the union of two sets, given n(A ∪ B) = n(A) + n(B) - n(A ∩ B), and calculate missing values for n(B) and n(A ∪ B).

Learn how to solve set theory problems using the formula for the union of two sets: n(A ∪ B) = n(A) + n(B) - n(A ∩ B). Example problems involve calculating n(B) and n(A ∪ B) with given data. Suitable for students in Grades 8-10.

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