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 $B$.

Title Cartesian product CartesianProduct 2013-03-22 11:48:56 2013-03-22 11:48:56 djao (24) djao (24) 10 djao (24) Definition msc 03-00 msc 81P10 msc 81P05 GeneralizedCartesianProduct