# Cartesian Product how can this be used in real life situations [closed]

I am learning about the cartesian product as defined by The New Oxford American Dictionary as:

the product of two sets: the product of set X and set Y is the set that contains all ordered pairs ( x, y) for which x belongs to X and y belongs to Y.

How can I use this in life? A simple practical example would help a lot.

• Ever seen $\mathbb{R^2}$, where we often draw graphs? – Christopher Jul 16 '15 at 0:49
• Once you explain the ways in which you are currently using the concept of a set in real life, we can figure out how the Cartesian product of sets is going to help you. – Zev Chonoles Jul 16 '15 at 0:50
• Some math books don't give real life situations where you can use it. They just show you the formula and how to calculate it. I am trying to find a way to use the concept in real life situations. – Robert Rocha Jul 16 '15 at 1:05
• any piece of information that requires two (or more) dependent or independent pieces of information can be seen as a cartesian product. – hjhjhj57 Jul 16 '15 at 2:07

A certain kind of Lacoste pullovers comes in five colors, three different neck forms, and in six sizes. Let \eqalign{C&:=\{{\rm blue,\ red,\ yellow,\ green,\ brown}\}\ ,\cr N&:=\{{\rm round\ neck, \ V{-} neck,\ polo{-}neck}\}\ ,\cr S&:=\{{\rm XS,\ S,\>M,\ L,\ XL,\ XXL}\}\cr} be the sets of colors, neck forms, and sizes, respectively. Then the set of all variants to be manufactured is the triple cartesian product $C\times N\times S$, and consists of $5\cdot 3\cdot 6=90$ elements. As a store manager selling this kind of sweater you would have to make room for $90$ heaps.