A PLC safety system is used for a milling machining center. When a machine tool is about to start its machining operation you need to make sure the workpiece is loaded and the safety guard is on. If the safety guard switch (X1) has not been activated and the limit switch (X2) signaling the presence of the workpiece has not been activated, a warning light (Y) will turn on. If only one of them is activated, the warning light still turns on. (a) Construct the truth table for this system. (b) Write the Boolean logic expression for the system. (c) Construct the ladder logic diagram for the system