Question

Three variable Boolean expression $PQ+PQR+\bar{P}Q+P\bar{Q}R$ can be written as

• A. $\bar{Q}+\bar{P}R$
• B. $\bar{P}+\bar{Q}R$
• C. $Q+PR$
• D. $Q+\bar{P}R$
• E. $P+QR$

Answer 1

Answer: (C)

$\because$ Given, boolean expression is
$=PQ+PQR+\bar{P}Q+P\bar{Q}R$
$=PQ(1+R)+\bar{P}Q+P\bar{Q}R$
$=PQ+\bar{P}Q+P\bar{Q}R(\because 1+R=1)$
$=Q(P+\bar{P})+P\bar{Q}R$
$=Q+PR\bar{Q}(\because P+\bar{P}=1)$
$=(Q+PR)(Q+\bar{Q})$
$=Q+PR(\because Q+\bar{Q}=1)$