Having trouble multiplying more than two sets together

• Aug 8th 2009, 11:59 PM
Roclemir
Having trouble multiplying more than two sets together

{1, 2} x {3, 4} = {(1, 3), (1, 4), (2, 3), (2, 4)}

but what if there's another set?

A x B x C = ???

if it were:

{1, 2} x {3, 4} x {5, 6}

how do these sets come together to give the cartesian product?
• Aug 9th 2009, 12:27 AM
Moo
Hello,

The cartesian product of n sets gives all the possible n-tuples, formed by 1 element of each.

So :
{1, 2} x {3, 4} x {5, 6} = {(1,3,5) , (1,3,6) , (1,4,5) , (1,4,6) , (2,3,5) , (2,3,6) , (2,4,5) , (2,4,6)}
• Aug 9th 2009, 02:46 AM
Plato
Quote:

Originally Posted by Roclemir
A x B x C = ???
if it were:
{1, 2} x {3, 4} x {5, 6}

$\{ 1,2\} \times \{ 3,4\} \times \{ 5,6\}$ $= \left\{ {(1,3,5),(1,3,6),(1,4,5),(1,4,6),(2,3,5),(2,3,6),( 2,4,5),(2,4,6)} \right\}$