Consider the two cascade $2$ to $1$ multiplexers as shown in the figure .
The minimal sum of products form of the output $X$ is
For $2 :1$ MUX, output $Y=S'I_o+SI_1$
So, output of MUX$1$ ,$f_1=P'0+PR =PR$
Output of MUX$2$ , $f_2=Q'R'+Qf_1=Q'R'+PQR$
which is option D
Answer : D
Lets say output of 1st multiplexer = m
table for 1st multiplexer
m = (P' * 0) + (P * R ) = PR ...(1)
table for 2nd multiplexer
X = (Q' * R') + (Q * m) ...(2)
put (1) in (2)
X=(Q' * R') + (Q * PR)
X= Q' R'+PQR
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