The Cartesian product of the sets $A$ and $B$, denoted by $A \times B$, is the set of all ordered pairs $(a, b)$, where $a$ is an element of the set $A$, and $b$ is an element of the set $B$.

In mathematical notation:

$A \times B = \{(a, b) \mid a \in A \text{ and } b \in B\}$

This means that the Cartesian product consists of all possible pairs where the first element comes from $A$ and the second element comes from $B$.

Would you like further explanation or examples?

Here are 5 related questions to expand on this topic:

1. How would you define the Cartesian product of three sets, $A \times B \times C$?
2. What is the Cartesian product of a set $A$ with itself, i.e., $A \times A$?
3. How does the Cartesian product differ from the union of sets?
4. What are some applications of Cartesian products in real-life scenarios or other mathematical fields?
5. If $A = \{1, 2\}$ and $B = \{3, 4\}$, what is $A \times B$?

Tip: The Cartesian product is foundational in creating coordinate systems, where elements from two sets combine to form points in a plane.