Question 5 (a) Use the rules of boolean algebra to simplify the following boolean expressions: i. abla+b)(+ 8) ii. (a + b) + (6 +aa)(a +7) [6] (b) Use the duality principle to find out the dual of the following equation: ab + c = (a + c)(a + 7)(b + c)(6+7) [2] (c) The lights in a classroom are controlled by two switches: one at the back and one at the front of the room. Moving either switch to the opposite position turns the light off if they were on and on if the were off. Assume the lights have installed so that when both switches are in the down position, the lights are off. Let P and Q be input to switches and R be the output (light on/off), design a circuit to control the witches and give its corresponding truth table. [6] (d) i. Fill in the following K-map for the Boolean function F(r. y. 2) = 7.7.5 +1.7.: + r.y.3 + :1.7.2 00 101 10 N 0 1 [3] ii. Use the previous K-map and find a minimisation, as the sum of three terms, of the expression F(x, y, 2) = 7.7.2 +7.7.2 + 1.7.7+19. (13