7. Consider the design of a burglar alarm for a house. When activated an alarm and lights will be activated to encourage the unwanted guest to leave. This alarm be activated if an unauthorized intruder is detected by window sensor and a motion detector. The window sensor is effectively a loop of wire that is a piece of thin metal foil that encircles the window. If the window is broken, the foil breaks breaking the conductor. This behaves like a normally closed switch. The motion sensor is designed so that when a person is detected the output will go on. As with any alarm an activate/deactivate switch is also needed. The inputs and outputs of the controller are itemized as follows e Output: A-Alarm and lights switch (1on) · Input: W-Window/Door sensor ( 1 OK) e Input: M-Motion Sensor (0 OK) Input: S-Alarm Active switch (1 on) · a) Draw a truth table to define the controller equation. b) Find the Boolean equation to define the controller equation using the truth table c) Draw the circuit and ladder program for the equatio