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.