Consider the following Boolean expression for $F$: $$F(P, Q, R, S) = PQ + \bar{P}QR + \bar{P}Q\bar{R}S$$ The minimal sum-of-products form of $F$ is

Factor out $Q$ from the expression:

Using the Boolean absorption/simplification rule $A + \bar{A}B = A + B$:

1. $P + \bar{P}(R + \bar{R}S) = P + R + \bar{R}S$

2. $R + \bar{R}S = R + S$

Substituting these back:

Now, multiply by $Q$:

This gives the minimal sum-of-products expression, matching option A.