Question

The statement $(p \Rightarrow q) \vee(p \Rightarrow r)$ is NOT equivalent to:

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

Answer 1

Answer: (B)

$ (p \rightarrow q) \vee(p \rightarrow r) $
$ (\sim p \vee q) \vee(\sim p \vee r) $
$ =\sim p \vee(q \vee r) $
$=p \rightarrow(q \vee r) \equiv(3) \text { is true. }$
Now (1) $( p \wedge \sim r ) \rightarrow q$
$ \sim( p \wedge \sim r ) \vee q =(\sim p \vee r ) \vee q $
$ =\sim p \vee( r \vee q )= p \rightarrow( q \vee r )$
(4) $( p \wedge \sim q ) \rightarrow r = p \rightarrow( q \vee r )$