Cartesian product
![](/Images/godic/202502/04/Cartesian_Product_qtl1.svg2101.png")
![Standard 52-card deck](/Images/godic/202502/04/Piatnikcards2101.jpg")
![Cartesian coordinates of example points](/Images/godic/202502/04/Cartesian-coordinate-system.svg2101.png")
![Example sets A=y∈ℝ:1≤y≤4, B=x∈ℝ:2≤x≤5, and C=x∈ℝ:4≤x≤7, demonstrating A×(B∩C)=(A×B)∩(A×C), A×(B∪C)=(A×B)∪(A×C), and A×(B\C)=(A×B)\(A×C).](/Images/godic/202502/04/CartDistr_svg.svg2102.png")
In mathematics, a Cartesian product is a mathematical operation which returns a set (or product set or simply product) from multiple sets. That is, for sets A and B, the Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B. Products can be specified using set-builder notation, e.g.