Question

The inverse of the proposition $(p \wedge \sim q)\rightarrow r$ is

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

Answer 1

Answer: (B)

$(\sim p) \vee q \rightarrow (\sim r)$

Answer 2

Given proposition is
$(p \wedge \sim q) \rightarrow r\,\,\,\,\,\,...(i)$
Inverse of E (i) is
$\sim(p \wedge \sim q) \rightarrow \sim r$
$\equiv \sim p \vee q \rightarrow \sim r$
$\equiv(\sim p) \vee q \rightarrow(\sim r)$