Number of Elements in Cartesian Product A × B
Question
If the set \( A \) has \( p \) elements and set \( B \) has \( q \) elements, then the number of elements in \[ A\times B \] is
(a) \( p+q \)
(b) \( p+q+1 \)
(c) \( pq \)
(d) \( p^2 \)
Solution
For every element of \( A \), there are \( q \) choices from set \( B \).
Thus, total ordered pairs in \[ A\times B \] are
\[ p\times q=pq \]
Hence, the correct answer is (c).