The given information states:

• $n(A \times B) = 667$ (the number of elements in the Cartesian product $A \times B$)
• $n(B) = 29$ (the number of elements in set $B$)

Formula for Cartesian Product:

$n(A \times B) = n(A) \times n(B)$

Substituting the values:

$667 = n(A) \times 29$

Solving for $n(A)$:

$n(A) = \frac{667}{29} = 23$

Thus, $n(A) = 23$.

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Related Questions:

1. What is the Cartesian product of two sets, and how is it defined?
2. If $n(A) = 15$ and $n(B) = 40$, what is $n(A \times B)$?
3. How does the Cartesian product behave when one of the sets is empty?
4. If $n(A \times B) = 900$ and $n(A) = 30$, find $n(B)$.
5. What are the practical applications of Cartesian products in mathematics?

Tip:

When working with set operations, always verify whether the sets involved are finite or infinite to ensure calculations make sense!