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Consider the following minterm expression for $F$:

$$F(P,Q,R,S) = \sum 0,2,5,7,8,10,13,15$$

The minterms $2$, $7$, $8$ and $13$ are 'do not care' terms. The minimal sum-of-products form for $F$ is

1. $Q \bar S+ \bar QS$
2. $\bar Q \bar S+QS$
3. $\bar Q \bar R \bar S+ \bar QR \bar S+Q \bar R S+QRS$
4. $\bar P \bar Q \bar S+ \bar P QS+PQS+P \bar Q \bar S$
edited | 959 views

While putting the terms to K-map the $3^{rd}$ and $4^{th}$ columns are swapped so, do $3^{rd}$ and 4th rows. So, term $2$ is going to $(0,3)$ column instead of $(0,2)$, $8$ is going to $(3,0)$ instead of $(2,0)$ etc.

Solving this k-map gives B) as the answer.

Reference: http://www.cs.uiuc.edu/class/sp08/cs231/lectures/04-Kmap.pdf

edited
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In the K-map column and row labels are not correct. Row labels must be P'Q', P'Q, PQ, PQ' and column labels must be R'S', R'S, RS, RS'.
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Sorry , i corrected.