You are told that the illumination of a Lamp L is controlled by three input X, Y, Z, L is to be on when either X or Y is on but not when they both on: L is to be on when Z is on if both X and Y are off, and L is to be on when Y is on except when all three are on. If any of these directions conflict, make a choice and state your choice. a) Write a logic equation and draw a circuit diagram of the described problem. b) Fill-in the truth table below Show a truth table for L. Simplify the following Boolean functions f(x, y) = x (x' + y) f(w, x, y, z) = (y + z')(y + z)