Question

write a java program that will perform the following.

Given two finite sets, list all elements in the Cartesian product of these two sets.

Given a finite set, list all elements of its power set.

Answer 1

Source Code in Java:

class Sets
{
static void cartesianProduct(int a[],int b[]) //method to print cartersian product of aXb
{
int i,j; //variables to loop through the arrays
for(i=0;i<a.length;i++)
{
for(j=0;j<b.length;j++)
System.out.print("("+a[i]+","+b[j]+")");
}
}
static void powerSet(int a[])
{
long size=(long)Math.pow(2,a.length); //calculating number of elements in the power set
int i,j;
for(i=0;i<size;i++)
{
for(j=0;j<size;j++)
{
if((i&(1 << j))>0)
System.out.print(a[j]+" ");
}
if(i==0) //if it is the first element, we print null
System.out.print("null");
if(i<size-1)
System.out.print(", ");
}
}
public static void main(String args[])
{
//testing the two functions
int a[]={1,2,3};
int b[]={4,5};
System.out.print("Carterian Product: ");
cartesianProduct(a,b);
System.out.println();
System.out.print("Power Set: ");
powerSet(a);
System.out.println();
}
}

Output: