$2-$A bulb in staircases has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and can be turned OFF by and one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles. a$)$ Construct a truth tableb$)$ From the truth table, construct the final function by using Miniterm.c$)$ Compare # c item with the output of K$-$ mapc$)$ e$)$ Construct the logic circuit for each of the essential inputs and for the final output