Which of the following represents the Cartesian product of sets A and B?

The Cartesian product of sets A and B is represented by the notation A × B. In set theory, the Cartesian product is defined as the set of all ordered pairs (a, b) where 'a' is an element from set A and 'b' is an element from set B. This creates a new set that combines every possible pairing of elements from the two sets, providing a comprehensive overview of how elements from each set can be matched.

For instance, if set A contains the elements {1, 2} and set B contains the elements {x, y}, then the Cartesian product A × B would result in the set {(1, x), (1, y), (2, x), (2, y)}. This method of pairing elements illustrates the fundamental concept behind the Cartesian product and is essential in various fields such as mathematics, computer science, and related disciplines.

The other concepts involved—intersection (A ∩ B), union (A ∪ B), and addition (A + B)—represent different operations on sets. Intersection refers to finding common elements, union combines all elements from both sets without duplicates, and addition can suggest combining cardinalities but does not correctly depict the relationship between two sets in terms of ordered pair