1. equals( "", "" )     = true
2. equals( "", X )      = false if X is not the empty string
3. equals( X, "" )      = false if X is not the empty string
4. equals( x+X, y+Y )   = false if x != y

Translation into Java

Of course there is an equals() method that is part of the class String. Let us forget this and write our own method. This should be merely a matter of translation:

  boolean equals( String strA, String strB )
  {
    // 1. equals( "", "" ) = true
    if       ( strA.length() ________ 0 && strB.length() ________ 0 )  
      return true;
      
    // 2. equals( "", X ) = false if X is not the empty string
    else if  ( strA.length() ________ 0 && strB.length() ________ 0 )  
      return false;
      
    // 3. equals( X, "" ) = false if X is not the empty string
    else if  ( strA.length() ________ 0 && strB.length() ________ 0 )  
      return false;
      
    // 4. equals( x+X, y+Y ) = false if x != y
    else if  ( strA.charAt(0) ________ strB.charAt(0) )         
      return false;
      
    // 5. equals( x+X, y+Y ) = true  if x == y and equals( X, Y )
    else
      return ________( strA.substring(1), strB.substring(1) ); 
  }

To detect an empty string, check if the length is zero. Remember that an empty string is a string that contains no characters. The value null is something different.