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

We are given:

• True minterms: $m(0, 5, 10, 15)$

• Don't care minterms: $d(2, 7, 8, 13)$

Plotting these on a 4-variable Karnaugh Map with variables $PQ$ for rows and $RS$ for columns:

• The four corner cells: $m_0 (0000)$, $d_2 (0010)$, $d_8 (1000)$, $m_{10} (1010)$. These 4 cells combine into a single group where $Q = 0$ and $S = 0$, giving the term $\overline{Q}\overline{S}$.

• The four cells: $m_5 (0101)$, $d_7 (0111)$, $d_{13} (1101)$, $m_{15} (1111)$. These 4 cells combine into a group where $Q = 1$ and $S = 1$, giving the term $QS$.

Both groups together cover all the required minterms $\{0, 5, 10, 15\}$.

Thus, the minimal SOP expression is:

Therefore, B is the correct option.