The problem asks to find \( n(A \times A \times B) \), where \( n(A) = 3 \) and \( n(B) = 4 \).

To solve this, we need to understand the Cartesian product. If \( A \times A \times B \) represents the Cartesian product of the sets \( A \), \( A \), and \( B \), then the number of elements in the Cartesian product is the product of the number of elements in each set.

The formula for the number of elements in a Cartesian product of sets is:

\[
n(A \times A \times B) = n(A) \times n(A) \times n(B)
\]

Substituting the given values:

\[
n(A \times A \times B) = 3 \times 3 \times 4 = 36
\]

Thus, \( n(A \times A \times B) = 36 \).

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. What is the general formula for the Cartesian product of multiple sets?
2. How does the Cartesian product differ from the union and intersection of sets?
3. How would the result change if \( n(A) = 5 \) and \( n(B) = 2 \)?
4. Can Cartesian products be performed on infinite sets? How would \( n(A \times A \times B) \) behave in that case?
5. What are some practical applications of the Cartesian product in real-life scenarios?

**Tip:** Always confirm the interpretation of the symbols in a problem, especially in set theory where notations can vary across contexts.

If n(A) = 3, n(B) = 4 then n(A × A × B) =

Discover how to calculate the number of elements in a Cartesian product of sets with the example n(A) = 3 and n(B) = 4. Learn the Cartesian product formula and apply it step-by-step to find n(A × A × B) = 36. This tutorial is ideal for students in Grades 6-8.

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