(Solved): Question 2a. [6 points] Boolean algebra. Problem Description: Suppose that we are given a circuit ...

Question 2a. [6 points] Boolean algebra. Problem Description: Suppose that we are given a circuit that implements an arbitrary Boolean function \( f(a, b, c) \), i.e. the circuit takes \( a, b, c \) as inputs and produces \( f \) as the output. If we invert the inputs, and simultaneously invert the output, do we always get back the same function? In other words, is \( f(\bar{a}, \bar{b}, \bar{c})=\overline{f(a, b, c)} \) ? Use only Boolean algebra to prove equality or inequality on the two Boolean functions below: Show your work! (a) (3 points) \( f(a, b, c)=a c+b \bar{c} \) Solution: (b) (3 points) \( f(a, b, c)=a \oplus(\bar{b} \bar{c}) \). Hint: Remember \( x \oplus y=x \bar{y}+\bar{x} y \) and \( x \bar{\oplus} y=\overline{x \oplus y} \). Solution: