Question

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

Answer 1

$Z=\overline{\overline{P\overline{Q}}.Q.\overline{Q.R}}=P\overline{Q}+\overline{Q}+\overline{\overline{Q.R}}$
$=P\overline{Q}+\overline{Q}+QR=\overline{Q}(P+1)+QR$
$=\overline{Q}+QR$
$=(\overline{Q}+Q).(\overline{Q}+R)=\overline{Q}+R$