There are $3$ rooms of $A,B$ and $C$ in the house, and each room contains a motion sensor$.$

If at least $2$ rooms are occupied, then the fan in the living room will be $ON(HIGH)$ automatically.

If a room is occupied, denotes it as $1$ and vice versa.

$($i$)$ Draw the truth table for the $3$ inputs and $1$ output.

$($ii$)$ Minimized the expression into simplified POS form using K$-$map.

$($iii$)$ Simplify and draw the logic circuit for the fan controls in the room

$($iv$)$ Verify your truth table with the constructed logic circuit $($Construct your circuit in circuitverse and screenshot your results$)$