The question is asking to find $n(A \cup B)$, which represents the number of elements in the union of sets $A$ and $B$. To solve this, we use the union rule in set theory, which is given by the formula:

$n(A \cup B) = n(A) + n(B) - n(A \cap B)$

We are provided with the following information:

• $n(A) = 10$
• $n(B) = 11$
• $n(A \cap B) = 6$

Now, substituting these values into the union rule:

$n(A \cup B) = 10 + 11 - 6 = 15$

So, $n(A \cup B) = 15$.

Let me know if you need further clarification or details!

Here are 5 related questions to explore this topic further:

1. What is the difference between the union and the intersection of two sets?
2. How would the union rule change if $A$ and $B$ were mutually exclusive sets?
3. Can you explain the meaning of $n(A \cap B) = 6$ in the context of sets?
4. How does this problem change if we have three sets instead of two?
5. What is the general formula for the union of multiple sets?

Tip: The union rule is a key concept in set theory, and it's particularly useful when analyzing problems with overlapping groups or categories.