Show how a power source, a lamp and a number of switches can be represent the following logical functions. Sketch the truth table of the functions. 1) L = A+ B + C 2)L = A middot B middot C 3) L = A middot B + C 4)L=A circledplus B Derive the Boolean expressions for the following arrangements using AND, OR and NOT operations. The output L is the state of the lamp. Derive a Boolean expression for the following circuit and sketch the true table. Draw the circuit diagrams using standard logic gates to implement the following expressions: 1) X = (A+B)^bar middot C 2) Y = AB^bar C + A^bar D+CD^bar 3) Z = Simplify the following Boolean expressions using Boolean algebra. Show the simplification steps. 1)X = (A+A^bar) + B 2)Y = ABC + A^bar BC + AC + AC^bar 3)Z = (A+C)(AD+ AD^bar) + AC + C 4) D = AB^bar(A^bar + B)(B + B^bar)