Simplified form of the Boolean function

$$ F(P, Q, R, S)=\bar{P} \bar{Q}+\bar{P} Q S+P \bar{Q} \bar{R} \bar{S}+P \bar{Q} R \bar{S} $$

is

For a $$3$$ -input logic circuit shown below, the output $$Z$$ can be expressed as

The Boolean expression $$AB + A\overline C + BC$$ simplifies to

Consider the following Sum of products expression, $$F.$$
$$F = ABC + \overline A \overline B C + A\overline B C + \overline A BC + \overline A \overline B \overline C $$

The equivalent Product of Sums expression is