In particular, Cartesian product of two sets is a set of ordered pairs, while the Cartesian product of three sets is a set of ordered triplets. Precisely, let A, B and C be three non-empty sets.

**Cartesian Product**

We know that the
Cartesian product of sets is nothing but a set of ordered elements. In
particular, Cartesian product of two sets is a set of ordered pairs, while the
Cartesian product of three sets is a set of ordered triplets. Precisely, let *A, B* and *C* be three non-empty
sets. Then the ** Cartesian product** of

Here *A* *×* *B* is a subset of R *×* R*.*
The number of elements in *A* *×* *B* is the product of the
number of elements in *A* and the number of
elements in *B*, that is, *n*(*A* *×* *B*)
= *n*(*A*)*n*(*B*), if *A* and *B* are finite. Further *n*(*A*
*×* *B* *×* *C*) = *n*(*A*)*n*(*B*)*n*(*C*),
if *A, B* and *C* are finite.

It is easy to see that
the following are the subsets of R *×* R.

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11th Mathematics : UNIT 1 : Sets, Relations and Functions : Cartesian Product | Definition, Formula, Solved Example Problems, Exercise | Mathematics

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