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The problem you're working on involves set theory, specifically the union and intersection of two sets \( A \) and \( B \). Here's a breakdown of the provided information:

- \( n(B) = 7 \) (the number of elements in set \( B \)),
- \( n(A \cap B) = 5 \) (the number of elements in the intersection of sets \( A \) and \( B \)),
- \( n(A \cup B) = 26 \) (the number of elements in the union of sets \( A \) and \( B \)).

You're asked to find \( n(A) \) (the number of elements in set \( A \)).

We can use the following formula for the union of two sets:

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

Now, substituting the given values into the equation:

\[
26 = n(A) + 7 - 5
\]

Simplifying the equation:

\[
26 = n(A) + 2
\]

Now, solving for \( n(A) \):

\[
n(A) = 26 - 2 = 24
\]

Thus, \( n(A) = 24 \).

Let me know if you have any further questions or would like additional details. Here are five related questions to explore this topic further:

1. How would the result change if \( n(A \cap B) \) were different?
2. Can you explain why the inclusion-exclusion principle is used here?
3. What happens if \( A \) and \( B \) are disjoint sets?
4. How would you calculate \( n(A \cup B \cup C) \) for three sets?
5. Can you solve for \( n(A) \) if only \( n(A \cup B) \) and \( n(B) \) are given?

**Tip**: When dealing with set theory problems, always check if the sets are overlapping or disjoint, as this affects the formula you need to use.

If n(B) = 7, n(A ∩ B) = 5 and n(A ∪ B) = 26, what is n(A)?

Solve for n(A) using set theory, given that n(B) = 7, n(A ∩ B) = 5, and n(A ∪ B) = 26. This problem covers core concepts like the union and intersection of sets, using the inclusion-exclusion principle to simplify the equation.

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