This is a java program to generate and print all the pair of subsets whose union makes the original set.

Here is the source code of the Java Program to Generate All Pairs of Subsets Whose Union Make the Set. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

`//This is a java program to generate all pair of subsets whose union results the original set`

import java.util.Random;

import java.util.Scanner;

public class Pair_Subset_Union_Set

`{`

public static int[] binary(int N)

`{`

int[] binary = new int[(int) Math.pow(2, N)];

for (int i = 0; i < Math.pow(2, N); i++)

`{`

int b = 1;

binary[i] = 0;

int num = i;

while (num > 0)

`{`

binary[i] += (num % 2) * b;

num /= 2;

b = b * 10;

`}`

`}`

return binary;

`}`

public static void main(String args[])

`{`

Random random = new Random();

Scanner sc = new Scanner(System.in);

System.out.println("Enter the number of elements in the set: ");

int N = sc.nextInt();

int[] sequence = new int[N];

for (int i = 0; i < N; i++)

sequence[i] = Math.abs(random.nextInt(100));

System.out.println("The elements in the set : ");

for (int i = 0; i < N; i++)

System.out.print(sequence[i] + " ");

int[] mask = new int[(int) Math.pow(2, N)];

mask = binary(N);

System.out

.println("\nThe pair of permutations whose union is original set are: ");

for (int i = 0; i < (Math.pow(2, N) / 2); i++)

`{`

System.out.print("{ ");

for (int j = 0; j < N; j++)

`{`

if (mask[i] % 10 == 1)

System.out.print(sequence[j] + " ");

mask[i] /= 10;

`}`

System.out.print("} and ");

System.out.print("{ ");

for (int j = 0; j < N; j++)

`{`

if (mask[(int) Math.pow(2, N) - 1 - i] % 10 == 1)

System.out.print(sequence[j] + " ");

mask[(int) Math.pow(2, N) - 1 - i] /= 10;

`}`

System.out.println("}");

`}`

sc.close();

`}`

`}`

Output:

$ javac Pair_Subset_Union_Set.java $ java Pair_Subset_Union_Set Enter the number of elements in the set: 5 The elements in the set : 3 47 97 79 8 The pair of permutations whose union is original set are: { } and { 3 47 97 79 8 } { 3 } and { 47 97 79 8 } { 47 } and { 3 97 79 8 } { 3 47 } and { 97 79 8 } { 97 } and { 3 47 79 8 } { 3 97 } and { 47 79 8 } { 47 97 } and { 3 79 8 } { 3 47 97 } and { 79 8 } { 79 } and { 3 47 97 8 } { 3 79 } and { 47 97 8 } { 47 79 } and { 3 97 8 } { 3 47 79 } and { 97 8 } { 97 79 } and { 3 47 8 } { 3 97 79 } and { 47 8 } { 47 97 79 } and { 3 8 } { 3 47 97 79 } and { 8 } Enter the number of elements in the set: 3 The elements in the set : 37 76 87 The pair of permutations whose union is original set are: { } and { 37 76 87 } { 37 } and { 76 87 } { 76 } and { 37 87 } { 37 76 } and { 87 }

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