Question

The compound statement $(P\vee Q)\wedge (\sim P)\Rightarrow Q$ is equivalent to :

• A. $P\vee Q$
• B. $\sim (P\Rightarrow Q)\iff P\wedge \sim Q$
• C. $P\wedge \sim Q$
• D. $\sim (P\Rightarrow Q)$

Answer 1

The correct option is B $\sim (P\Rightarrow Q)\iff P\wedge \sim Q$

$P\wedge Q)\wedge (\sim P)\to Q$
$=\sim (P\vee Q)\vee P\vee Q$
$=\sim (P\vee Q)\vee (P\vee Q)\Rightarrow$ It is a tautology.
Only option (2) is a tautology because
$\sim (P\to Q)=\sim (\sim P\vee Q)=P\wedge \sim Q$