output

Question

Answer 1

$Z= \overline{\overline{(P\bar Q)}.Q.\overline{QR}}$

$Z=\overline{\overline{P\bar Q}}+\bar Q+\overline{\overline{QR}}$

$Z=P\bar Q+\bar Q+QR$

$Z=\bar Q(1+P)+QR$

$Z=\bar Q+QR$

Apply distributive law:

$Z=(Q+\bar Q)(\bar Q+R)$

$Z=(\bar Q+R)$