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Cartesian product
For any sets $A$ and $B$, the Cartesian product $A\times B$ is the set consisting of all ordered pairs $(a,b)$ where $a\in A$ and $b\in B$.
The Cartesian product satisfies the following properties, for all sets $A$, $B$, $C$, and $D$:

$A\times\emptyset=\emptyset$

$(A\times B)\cap(C\times D)=(A\cap C)\times(B\cap D)$

$(A\times B)^{\complement}=(A^{\complement}\times B^{\complement})\cup(A^{% \complement}\times B)\cup(A\times B^{\complement})$
Here $\emptyset$ denotes the empty set, $\cap$ denotes intersection, $\cup$ denotes union, and ${}^{\complement}$ denotes complement with respect to some universal set $U$ containing $A$ and $B$.
Related:
GeneralizedCartesianProduct
Type of Math Object:
Definition
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