Practice 3 1. Prove the identity of each of the following Boolean equations using algebraic manipulation: (c) AD' + A'B + C'D + B,C = (A'+B'+C'+D') (A+B+C+D) 2. Draw the logic diagram and truth table for the following functions: (b) F2-(A +B'+C'+D') (A+B+C+D) 3. Given that A.B-0 and A+B-1, prove that 4. Consider an example Boolean equation representing electrical or electronic logic for control of the lowering of the driver's power window in a car. The window is raised or lowered by a motor driving a lever mechanism connected to the window. Output: L-1 means that the window motor is powered up to turn in the direction that lowers the window, L=0 means that the window motor is not powered up. Inputs: D-1 means that the lowering of the driver's window is requested, D=0 means that the action is not requested. X is the output of a mechanical limit switch. X-1 if the window is at limit, X=0 if the window is not at limit. Draw the truth table and formulate an equation to implement the operation