Question
The inverse of the statement $$\left( {p \, \wedge \sim q} \right) \to r{\text{ is}}$$
A.
$$ \sim \left( {p \, \vee \sim q} \right) \to \, \sim r$$
B.
$$\left( { \sim p \wedge q} \right) \to \, \sim r$$
C.
$$ \left( { \sim p \vee q} \right) \to \, \sim r$$
D.
None of these
Answer :
$$ \left( { \sim p \vee q} \right) \to \, \sim r$$
Solution :
The inverse of the proposition $$\left( {p \, \wedge \sim q} \right) \to r{\text{ is }} \sim \left( {p \, \wedge \sim q} \right) \to \, \sim r$$
$$\eqalign{
& \equiv \,\, \sim p \, \vee \sim \left( { \sim q} \right) \to \, \sim r \cr
& \equiv \,\, \sim p \vee q \to \, \sim r \cr} $$