Question

The statement pattern $(\sim p \wedge q)$ is logically equivalent to

• A. $(p \vee q) \vee \sim p $
• B. $(p \vee q) \wedge \sim p $
• C. $(p \wedge q) \to p $
• D. $(p \vee q) \to p $

Answer 1

Answer: (B)

$B \rightarrow( p \vee q ) \wedge \sim p =( p \wedge \sim p ) \vee( q \wedge \sim p ) \ldots $ Distributive law
$= F \vee q (\wedge \sim p ) \ldots $ Complementary law
$= q \wedge \sim p \ldots $ Identify law
$=\sim p \wedge q \ldots $ Commutative law
Hence, $\sim p \wedge q$ is equivalent to $( p \vee q ) \wedge \sim p$