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बूलीय व्यंजक (Boolean expression) $(( p \wedge q ) \vee( p \vee \sim q )) \wedge(\sim p \wedge \sim q )$ निम्न में जिसके तुल्य है, वह है
$p \wedge q$
$p \wedge \left( { \sim q} \right)$
$\left( { \sim p} \right) \wedge \left( { \sim q} \right)$
$p \vee \left( { \sim q} \right)$
Solution
$\left( {\left\{ {\left( {p \wedge q} \right) \vee p} \right\} \vee \left\{ {\left( {p \wedge q} \right) \vee \sim q} \right\}} \right) \wedge \sim \left( {p \vee q} \right) \equiv $
$\left\{ {p \vee \left( {p \vee \sim q} \right) \wedge \left( {q \vee \sim q} \right)} \right\} \wedge \sim \left( {p \vee q} \right)$
$\left( {p \vee \left\{ {p \vee \sim q} \right\}} \right) \wedge \left( {p \vee q} \right) \equiv \left( {p \vee \sim q} \right) \wedge \sim \left( {p \vee q} \right) \equiv \sim p \wedge \sim q$
