A client wants us to develop a security alarm system for their house. The entry points to the house are: Front door (F = 0 if the door is closed, F=1 if the door is open) Garden-level window (W = 0 if the window is closed, W=1 if the window is open) Back yard gate (G = 0 if the gate is closed, G=1 if the gate is open) Also, there is a sensor (S) inside the house that can identify if anyone is home or not. This sensor, returns 1 if there is someone in the house and 0 otherwise. Develop a logical function X that returns 1 if any of these happen: . There is no one home and the backyard gate is open (regardless of the state of F and W) . There is no one home and the garden level window is open (regardless of the state of F and G) . Front door and backyard gate are both open (regardless of the state of S and W) Draw an optimal NOR implementation of the circuit by using NOR gates of 2 or 3 inputs. Your solution must include:1. The truth with the this exact heading: "Inn\" 2. Iiimap with all the loops drawn on it: GR 3. Optimal Pee expression 4. The t~i+'CiRreact'3..r expression 5. The circuit drawing [please keep it new tidy and neat} 6. Final gate count