Sets

Cartesian product

Keywords: sets, cartesian product, cartesian square

Cartesian product

A×B=a,b:aA, bB

The Cartesian Product of two sets A and B is the set of all Ordered Pairs (a,b)  where the first element of order pairs a belongs to first set A and second element of ordered pairs b belongs to second set B.

Example:A={1,3,6}, B={x,y} AxB=1,x,1,y,3,x,3,y,6,x,6,y

Cartesian square

A2=AxA=a,b: aA, bB

The Cartesian squere of set A is the set of all Ordered Pairs (a,b)  where both elements of order pairs belongs to first set A.

Example:A={1,3,6} AxA=1,1,1,3,1,6,3,1,3,3,3,6,6,1,6,3,6,6

Properties of Cartesian Product

A=m, B=n AxB=m·n
A= B= AxB=