2. A room contains a safe. There is one door into the room, and there is one window. An alarm must be constructed so when the safe is open, the alarm will sound if the door is open or the window is open (and not otherwise), but when the safe is closed, it will sound only if the window is open and the door is closed, and not otherwise. Let S, W, D denote the state of the safe, window and door respectively, being 0 if it is open and 1 if it is closed. Let A denote the state of the alarm, being 1 if it is sounding and 0 if it is silent. (a) Complete the input / output table at right describing the alarm system. (b) Find a Boolean expression that has this input /output table. (0) Indicate by shading the region on the Venn diagram at right that S\"? \"PM Bow form corresponds to the alarm sound ing. Use this to simplify your Boolean expression. $1. \"MAG\" 09w