Question

P, Q, and R represent switches in on position and P’, Q’ and R’ represent switches in off position. Construct a switching circuit representing the polynomial PR + Q (Q’ + R) (P + QR). Using Boolean Algebra, simplify the polynomial expression and construct the simplified circuit. 

Answer 1

The switching circuit of the given polynomial is :

The given polynomial can be  simplified as :

PR + Q (Q' + R) (P + QR) = PR + (QQ' + QR) (P +QR)

= PR + (O + QR) (P + QR)

= PR + QR (P + OR) = PR + QR (QR + P)

= PR + QR                 ...[ ∵ a ( a + b ) = a ]

⇒ The light is on when the switches P and R are on or when the switches Q and R are on.

The equivalent switching circuit is :