The simplified SOP (Sum of Product) from the Boolean expression
$(P + \bar{Q} + \bar{R}) . (P + \bar{Q} + R) . (P + Q +\bar{R})$ is

Question

The simplified SOP (Sum of Product) from the Boolean expression $(P + \bar{Q} + \bar{R}) . (P + \bar{Q} + R) . (P + Q +\bar{R})$ is

Accepted Answer

Correct answer: B — Simplified result: P + ¬Q·¬R Step 1: Use (X+Y)(X+Z) = X + YZ with X = (P+¬Q), Y = ¬R, Z = R to simplify (P+¬Q+¬R)(P+¬Q+R) to (P+¬Q). Step 2: Apply (X+Y)(X+Z) = X + YZ again with X = P, Y = ¬Q, Z = (Q+¬R): This gives P + ¬Q·(Q + ¬R) = P + (¬Q·Q) + (¬Q·¬R) = P + 0 + ¬Q·¬R = P + ¬Q·¬R. Therefore the simplified SOP form is P + ¬Q·¬R.

Answer

A. $(\bar{P}.Q+\bar{R})$

Answer

B. $(P+\bar{Q}.\bar{R})$

Answer

C. $(\bar{P}.Q+R)$

Answer

D. $(P.Q+R)$

The simplified SOP (Sum of Product) from the Boolean expression \((P + \bar{Q}…