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 $($C$)$

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 tum 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$)$