Question

The inverse of the proposition $(p\mspace{6mu} \land \sim q) \Rightarrow r$ is

• A. $\sim r \Rightarrow \mspace{6mu}\sim p \vee q$020.000
• B. $\sim p \vee q \Rightarrow \mspace{6mu}\sim r$
• C. $r \Rightarrow p\mspace{6mu} \land \sim q$
• D. None of these

Answer 1

Answer: (B)

$\sim p \vee q \Rightarrow \mspace{6mu}\sim r$

Answer 2

Inverse of $p \Rightarrow q$ is $\sim p \Rightarrow \mspace{6mu}\sim q$

∴ inverse of $(p\mspace{6mu} \land \sim q) \Rightarrow r$ is

$\sim(p\mspace{6mu} \land \sim q) \Rightarrow \mspace{6mu}\sim r$ i.e. $(\sim p \vee q) \Rightarrow \mspace{6mu}\sim r$.