(a) Use truth table to prove the following: ABC + ABC + ABC + ABC = (A+B+C)(A+B+C)(A+B+C)(A+B+C) (b) Design a digital circuit that implements the Boolean function F below using AND, OR, NOT gates ONLY. Do not change the form of the Boolean equation. F(x, y, z) = (xz+xy+yz)(x+y) (y + z) Question 2: A combinational circuit is defined by the following three Boolean functions: F1=ABC F2 = A'B+ AC F3 AB+B'C Design the circuit with a decoder and external gates. Question 3: Implement the logic function F = w'xy + wx' + wxy' with the following component constraints: (a) Use one 4-to-1 multiplexer and one invertor. (b) Use one 2-to-1 multiplexer and one 2-inputs XOR gate. Question 3: Implement the logic function F = w'xy + wx' + wxy' with the following component constraints: (a) Use one 4-to-1 multiplexer and one invertor. (b) Use one 2-to-1 multiplexer and one 2-inputs XOR gate. ~ End of Assignment 3 ~ Question 2: A combinational circuit is defined by the following three Boolean functions: F = ABC F2 A'BAC F3 = AB+B'C Design the circuit with a decoder and external gates.