# Cartesian Product of Two Sets

Let A and B be two sets, Cartesian productA × B is the set of all ordered pair of elements from A and B
A × B = {{x, y} : x ∈ A, y ∈ B}

Let A = {a, b, c} and B = {d, e, f}
The Cartesian product of two sets is
A x B = {a, d}, {a, e}, {a, f}, {b, d}, {b, e}, {b, f}, {c, d}, {c, e}, {c, f}}

A has 3 elements and B also has 3 elements. The Cartesian Product has 3 x 3 = 9 elements.

In general, if there are m elements in set A and n elements in B, the number of elements in the Cartesian Product is m x n

Given two finite non-empty sets, write a program to print Cartesian Product.

Examples :

```Input : A = {1, 2}, B = {3, 4}
Output : A × B = {{1, 3}, {1, 4}, {2, 3}, {2, 4}}

Input  : A = {1, 2, 3} B = {4, 5, 6}
Output : A × B = {{1, 4}, {1, 5}, {1, 6}, {2, 4},
{2, 5}, {2, 6}, {3, 4}, {3, 5}, {3, 6}}
```

## CPP

 `// C++ Program to find the Cartesian Product of Two Sets ` `#include ` ` `  `void` `findCart(``int` `arr1[], ``int` `arr2[], ``int` `n, ``int` `n1) ` `{ ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``for` `(``int` `j = 0; j < n1; j++) ` `            ``printf``(``"{%d, %d}, "``, arr1[i], arr2[j]); ` `} ` ` `  `int` `main() ` `{ ` `    ``int` `arr1[] = { 1, 2, 3 }; ``// first set ` `    ``int` `arr2[] = { 4, 5, 6 }; ``// second set ` `    ``int` `n1 = ``sizeof``(arr1) / ``sizeof``(arr1); ` `    ``int` `n2 = ``sizeof``(arr2) / ``sizeof``(arr2); ` `    ``findCart(arr1, arr2, n1, n2); ` `    ``return` `0; ` `} `

## Java

 `// Java Program to find the  ` `// Cartesian Product of Two Sets ` `import` `java.io.*; ` `import` `java.util.*; ` ` `  `class` `GFG { ` ` `  `    ``static` `void` `findCart(``int` `arr1[], ``int` `arr2[],  ` `                                    ``int` `n, ``int` `n1) ` `    ``{ ` `        ``for` `(``int` `i = ``0``; i < n; i++) ` `          ``for` `(``int` `j = ``0``; j < n1; j++) ` `            ``System.out.print(``"{"``+ arr1[i]+``", "` `                             ``+ arr2[j]+``"}, "``); ` `    ``} ` `    ``// Driver code ` `    ``public` `static` `void` `main (String[] args) { ` `         `  `        ``// first set ` `        ``int` `arr1[] = { ``1``, ``2``, ``3` `};  ` `         `  `        ``// second set ` `        ``int` `arr2[] = { ``4``, ``5``, ``6` `};  ` `         `  `        ``int` `n1 = arr1.length; ` `        ``int` `n2 = arr2.length; ` `        ``findCart(arr1, arr2, n1, n2); ` `    ``} ` `} ` ` `  ` `  `// This code is contributed by Nikita Tiwari. `

## Python3

 `# Python3 Program to find the ` `# Cartesian Product of Two Sets ` ` `  `def` `findCart(arr1, arr2, n, n1): ` ` `  `    ``for` `i ``in` `range``(``0``,n): ` `        ``for` `j ``in` `range``(``0``,n1): ` `            ``print``(``"{"``,arr1[i],``", "``,arr2[j],``"}, "``,sep``=``"``",end="``") ` ` `  `# Driver code ` `arr1 ``=` `[ ``1``, ``2``, ``3` `] ``# first set ` `arr2 ``=` `[ ``4``, ``5``, ``6` `] ``# second set ` ` `  `n1 ``=` `len``(arr1) ``# sizeof(arr1) ` `n2 ``=` `len``(arr2) ``# sizeof(arr2); ` ` `  `findCart(arr1, arr2, n1, n2); ` ` `  `# This code is contributed ` `# by Smitha Dinesh Semwal `

## C#

 `// C# Program to find the  ` `// Cartesian Product of Two Sets ` `using` `System; ` ` `  `class` `GFG { ` ` `  `    ``static` `void` `findCart(``int` `[]arr1, ``int` `[]arr2,  ` `                                    ``int` `n, ``int` `n1) ` `    ``{ ` `        ``for` `(``int` `i = 0; i < n; i++) ` `            ``for` `(``int` `j = 0; j < n1; j++) ` `                ``Console.Write(``"{"` `+ arr1[i] + ``", "` `                                ``+ arr2[j] + ``"}, "``); ` `    ``} ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `Main () { ` `         `  `        ``// first set ` `        ``int` `[]arr1 = { 1, 2, 3 };  ` `         `  `        ``// second set ` `        ``int` `[]arr2 = { 4, 5, 6 };  ` `         `  `        ``int` `n1 = arr1.Length; ` `        ``int` `n2 = arr2.Length; ` `         `  `        ``findCart(arr1, arr2, n1, n2); ` `    ``} ` `} ` ` `  ` `  `// This code is contributed by vt_m. `

## PHP

 ` `

Output :

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

Practical Examples:
1) A set of playing cards is Cartesian product of a four element set to a set of 13 elements.

2) A two dimensional coordinate system is a Cartesian product of two sets of real numbers.

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