Step-by-step Solution:

Let ( n(x) ) denote the number of elements in set ( X ). If ( n(A) = p ) and ( n(B) = q ), then how many ordered pairs ((a, b)) are there with ( a \(\in\) A ) and ( b \(\in\) B )? \[\] The number of ordered pairs ((a, b)) can be formed by selecting any element (a) from (A) and any element (b) from (B). There are (p) choices for (a) and (q) choices for (b). \[\] The total number of ordered pairs is given by the product of these choices: \[\] n(A) \(\times\) n(B) = p \(\times\) q \[\] \[\] \[\] Correct Option: (b)