The function corresponding to the Bode plot of Figure, is

For a flip-flop formed from two $$NAND$$ gates as shown in figure. The unusable state corresponds to

The logic function $$f = \overline {\left( {x.\overline y } \right) + \left( {\overline x .y} \right)} $$ is the same as

The logic function $$F = AC + ABD + ACD$$ is to be realized using an $$8$$ to $$1$$ multiplexer shown in figure, using $$A, C$$ and $$D$$ as control inputs.

$$(a)$$ Indicate the inputs to be applied at the terminals $$0$$ to $$7.$$
$$(b)$$ Can the function be realize using a $$4$$ to $$1$$ multiplexer?
State YES or NO.