Implement the following method.

In this lab, a binary relation is represented using a boolean matrix (double array of booleans) as follows.

Recall that A={a1,an} and RAA is a relation on A.

We represent a binary relation R using a matrix MR, where MR[i][j]=true means that (ai+1,aj+1)R, and MR[i][j]=false means that (ai+1,aj+1)R. (Note there is an off by one thing going on here. Our set starts couning elements at 1 but double arrays in Java are indexed starting at 0.)

public class Relations {
	/**
	* Returns composition of R and S. Return relation T such that if (i, j) in R and (j, k) in S then (i, k) in T.
	* @param S relation, represented as a matrix (double array)
	* @param R relation, represented as a matrix (double array)
	* @return S composed with R
	*/
	public static boolean[][] compose(boolean[][] R, boolean[][] S) {
	// compare matrix sizes and make sure they agree: if R is n1 x n2 then S should be n2 x n3.
	int n1 = R.length;
	int n3 = S.length;
	if (n1 == 0 || n3 == 0) throw new UnsupportedOperationException("expecting non-empty arrays!");
	int n2 = R[0].length;
	int n4 = S[0].length;
	if (n2 == 0 || n4 == 0) throw new UnsupportedOperationException("expecting non-empty arrays!");
	if (n2 != n3) throw new UnsupportedOperationException("Number of columns of R must match number of rows of S");
	throw new UnsupportedOperationException("implement me!");
	}