QUESTION $2$

You are to design a combinational circuit that controls the lights in a room with multiple switches. The requirements are as follows.

There are $3$ switches in the room at different sides $-$ one at the front door $($A$),$ one at the side door $(B)$ and another at the back door $)$

In the initial state, the room lights are OFF. Additionally, the switch at the front door is ON whilst the others are OFF.

From the initial state, flipping any switch position will turn the lights ON$.$ Flipping any switch position again will turn the lights OFF and so on$.$

$($i$)$ Draw the truth table, for the inputs and outputs above $($ii$)$

Derive the final Boolean expression from the truth table.

$($iii$)$ Simplify your Boolean expression $($if possible$)$ and then draw the logic circuit for the switch controls in the room