Answer
a) $\neg $(p $\land$ ( q $ \lor $ $\neg$ r))
b) (( $\neg$ p) $\land$ ( $\neg$ q)) $\lor$(p $\land$ r)
Work Step by Step
a) Starting from the left.
First, the output of the Not gate is : $\neg$ r
The output of the OR gate is: q $ \lor $ $\neg$ r.
The output of the AND gate is p $\land$ ( q $ \lor $ $\neg$ r).
Therefore the output of this circuit is
$$\neg (p \land ( q \lor \neg r)).$$
b) The output of the top two Not gates is $\neg$ p and $\neg$ q.
Then ,the output of the top AND gate is ( $\neg$ p) $\land$ ( $\neg$ q). The output of the bottom AND gate is p $\land$ r.
Therefore, the output of this circuit is
$$(( \neg p) \land ( \neg q)) \lor (p \land r).$$
