Definition: The Cartesian product of the sets \(A\) and \(B\), \(A \times B\), is the set of all ordered pairs \((a, b)\), where \(a \in A\) and \(b \in B\). That is: \(A \times B = \{(a, b) \mid (a \in A) \land (b \in B)\}\). The Cartesian product of the sets \(A_1, A_2, \ldots ,A_n\), denoted by \(A_1 \times A_2 \times \cdots \times A_n\), is the set of ordered n-tuples \((a_1, a_2,...,a_n)\), where \(a_i\) belongs to \(A_i\) for \(i = 1, 2,\ldots,n\). That is, \[A_1 \times A_2 \times \cdots \times A_n = \{(a_1, a_2,\ldots,a_n) \mid a_i \in A_i \textrm{ for } i = 1, 2,\ldots,n\}\]