MCQ
The Boolean Expression $(p \wedge \sim q) \vee q \vee(\sim p \wedge q)$ is equivalent to :
- Ap ^ q
- ✓p v q
- C$p \vee \sim q$
- D$\sim p \wedge q$
✓
Answer
Correct option: B.
p v q
(B)
$(p \wedge \sim q) \vee q \vee(\sim p \wedge q)$
$\equiv[(p \vee q) \wedge(\sim q \vee q)] \vee(\sim p \wedge q)$...[Distributive law]
$\equiv[(p \vee q) \wedge T] \vee(\sim p \wedge q)$...[Complement law]
$\equiv(p \vee q) \vee(\sim p \wedge q)$ ...[Identity law]
$\equiv(p \vee q \vee \sim p) \wedge(p \vee q \vee q)$...[Distributive law]
$\equiv(T \vee q) \wedge(p \vee q)$...[Complement law and Idempotent law]
$\equiv T \wedge( p \vee q )$...[Identity law]
$\equiv p \vee q$...[Identity law]
$(p \wedge \sim q) \vee q \vee(\sim p \wedge q)$
$\equiv[(p \vee q) \wedge(\sim q \vee q)] \vee(\sim p \wedge q)$...[Distributive law]
$\equiv[(p \vee q) \wedge T] \vee(\sim p \wedge q)$...[Complement law]
$\equiv(p \vee q) \vee(\sim p \wedge q)$ ...[Identity law]
$\equiv(p \vee q \vee \sim p) \wedge(p \vee q \vee q)$...[Distributive law]
$\equiv(T \vee q) \wedge(p \vee q)$...[Complement law and Idempotent law]
$\equiv T \wedge( p \vee q )$...[Identity law]
$\equiv p \vee q$...[Identity law]
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