bool a: [0,0] true; (0,1) false; [1,1] true; (1,2] false; (2,4) true;
bool b: [0,1] true; (1,2) false; [2,3] true; (3,4) false;

// [0.0,0.0]TT; (0.0,1.0)FT; [1.0,1.0]TT; (1.0,2.0)FF; [2.0,2.0]FT; (2.0,3.0)TT; [3.0,3.0]TT; (3.0,4.0)TF; 
bool c: [0.0,0.0]true; (0.0,1.0)false; [1.0,1.0]true; (1.0,2.0)false; [2.0,2.0]false; (2.0,3.0)true; [3.0,3.0]true; (3.0,4.0)true; 
bool d: [0.0,0.0]true; (0.0,1.0)true;  [1.0,1.0]true; (1.0,2.0)false; [2.0,2.0]true;  (2.0,3.0)true; [3.0,3.0]true; (3.0,4.0)false; 

