Question

In java please

Program 5.1: Properties of a Relation Write a program that can determine which, if any, of the following properties a binary matrix exhibits: symmetric anti-symmetric asymmetric (from the textbook) reflexive or anti-reflexive (or neither of course) Program Requirements: Hard code at least 4 binary matrices all of size 4x4. Display each binary matrix and the the properties it exhibits. For example: A 0 100 0 00 0 0000 0 000 A anti-reflexive, anti-symmetric, asymmetric B 11 10 1000 1000 000 0 B-symmetric C 1 1 0 1 1011 1011 0 1 10 C none and so on for at least 4 binary matrices Additional Requirements: You can hard code the matrices but DO NOT hard code the properties. The program must determine the properties. I should be able to change the values of your matrix and get a different answer Do NOT use my example matrices Test Cases not required but you should know the expected output. Calculate it in advance and make sure the program is generating the expected output

Answer 1

package abc;

public class Main {
  
   // Fills transpose of mat[4][4] in tr[4][4]
   static void transpose(int mat[][], int tr[][])
   {
   for (int i = 0; i < 4; i++)
   for (int j = 0; j < 4; j++)
   tr[i][j] = mat[j][i];
   }
  
   static // Returns true if mat[][N] is symmetric, else false
   boolean isSymmetric(int mat[][])
   {
   int tr[][] = new int[4][4];
   transpose(mat, tr);
   for (int i = 0; i < 4; i++)
   for (int j = 0; j < 4; j++)
   if (mat[i][j] != tr[i][j])
   return false;
   return true;
   }
  
   static boolean isAntiSymmetric(int mat[][])
   {
   int tr[][] = new int[4][4];
   transpose(mat, tr);
   for (int i = 0; i < 4; i++)
   for (int j = 0; j < 4; j++)
   if (mat[i][j] != -tr[i][j])
   return false;
   return true;
   }
  
   static boolean isReflexive(int mat[][])
   {
   for (int i = 0; i < 4; i++) {
       for (int j = 0; j < 4; j++) {
           if (i==j) {
               if(mat[i][j] == 1){
                   return true;
               }
               else{
                   return false;
               }
           }
           else{
               return false;
           }
       }
   }
       return false;
  
  
     
   }

   public static void main(String[] args) {
       int[][] A = {{0, 1, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}};
       int[][] B = {{1, 1, 1, 0}, {1, 0, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 0}};
       int[][] C = {{1, 1, 0, 1}, {1, 0, 1, 1}, {1, 0, 1, 1}, {0, 1, 1, 0}};
       if (isSymmetric(A)) {
   System.out.println("Symmetric");
       }
   else{
       System.out.println ( "Asymmetric");
   }
       if (isAntiSymmetric(A)){
           System.out.println(" Anti-Symmetric");
       }
       if (isReflexive(A)){
           System.out.println("Reflexive");
       }
       if (isSymmetric(B)) {
   System.out.println("Symmetric");
       }
   else{
       System.out.println ( "Asymmetric");
   }
       if (isAntiSymmetric(B)){
           System.out.println(" Anti-Symmetric");
       }
       if (isReflexive(B)){
           System.out.println("Reflexive");
       }
      
       if (isSymmetric(C)) {
   System.out.println("Symmetric");
       }
   else{
       System.out.println ( "Asymmetric");
   }
       if (isAntiSymmetric(C)){
           System.out.println(" Anti-Symmetric");
       }
       if (isReflexive(C)){
           System.out.println("Reflexive");
       }
  
      
      
   }
}