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  4. Three variable Boolean expression PQ + PQR + barP Q + P barQ R can be written as

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

KEAMKEAM 2018Semiconductor Electronics: Materials Devices and Simple Circuits

Solution:

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