An $81$ multiplexer has inputs $A,B,$ and $C$ connected to the selection inputs $S_2,S_1,$ and $S_0,$ respectively. The data inputs, $I_0$ through $I_7,$ are as follows: $I_7=I_2=I_7=0$;$I_3=I_5=1$;$I_0=I_4=D$; and $I_6=D^{\text{'}}$ It implement the following function:

Select one:

a$.F={\displaystyle \underset{?}{\overset{?}{}}}m(1,6,7,9,10,11,12)$

b$.F={\displaystyle \underset{?}{\overset{?}{}}}m(1,6,7,9,10,11,15)$

c$.F={\displaystyle \underset{?}{\overset{?}{}}}m(1,6,7,9,10,11,12,13)$

d$.F={\displaystyle \underset{?}{\overset{?}{}}}m(1,6,8,9,10,11,12)$