CA×B

CA×B refers to the Cartesian product of two sets, A and B. The Cartesian product is a mathematical operation that results in a new set containing all possible ordered pairs where the first element of each pair is an element of the first set (A), and the second element of each pair is an element of the second set (B). If set A has 'm' elements and set B has 'n' elements, then the Cartesian product A×B will have m × n elements.

For example, if A = {1, 2} and B = {a, b, c}, then the Cartesian product A×B would be the set {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)}. Each element in A×B is an ordered pair, meaning the order matters. Therefore, A×B is generally not the same as B×A. The concept of the Cartesian product is fundamental in set theory and has wide applications in various fields, including algebra, discrete mathematics, and computer science, particularly in defining relations and functions. It forms the basis for creating coordinate systems, such as the Cartesian coordinate system, which is essential for graphing and geometry.