Cartesian Product

Definition

$A\times B=\{(a,b)|a\in A\wedge b\in B\}$ where $A,B$ are sets

The set of all ordered pairs $(a,b)$ where $a\in A\wedge b\in B$

Facts

$A\times \varnothing =\varnothing \times A=\varnothing$

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

$A\times (B-C)=(A\times B)-(A\times C)$