The diagram of a logic circuit is given below. The output `F` of the circuit is represented by

Options

A. `P + R.Q`
B. `P.(R.Q)`
C. `P.(R +Q)`
D. `P + (R + Q)`

Answer

A

Explanation

Output of upper OR gate = P + R Output of lower OR gate = P + Q
`therefore` Net output A = (P + R). (P + Q) = P.P + P.Q + R.P + R.Q
= P. (1 + Q) + R. P + R. Q
`therefore 1 + Q = 1` and `P.P = P`
`therefore` A = P + R. P + R.Q = P(1 + R) + RQ = P + RQ