If P and Q are two statements, then which of& | vedclass

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Question

$LHS$ of all the options are some i.e.

$((P \rightarrow Q) \wedge \sim Q)$

$\equiv(\sim P \vee Q ) \wedge \sim Q$

$\equiv(\sim P \wedge \sim

Vedclass · Accepted Answer

$(( P \Rightarrow Q ) \wedge \sim Q ) \Rightarrow \sim P$

Vedclass · Answer

$LHS$ of all the options are some i.e.

$((P ightarrow Q) \wedge \sim Q)$

$\equiv(\sim P \vee Q ) \wedge \sim Q$

$\equiv(\sim P \wedge \sim Q ) \vee( Q \wedge \sim Q )$

$\equiv \sim P \wedge \sim Q$

$(A)$ $(\sim P \wedge \sim Q) ightarrow Q$

$\equiv \sim(\sim P \wedge \sim Q) \vee Q$

$\equiv(P \vee Q) \vee Q 
eq$ tautology

$(B)$ $(\sim P \wedge \sim Q) ightarrow \sim P$

$\equiv \sim(\sim P \wedge \sim Q ) \vee \sim P$

$\equiv( P \vee Q ) \vee \sim P$

$(C)$ $(\sim P \wedge \sim Q) ightarrow P$

$\equiv(P \vee Q) \vee P 
eq$ Tautology

$(D)\,(\sim P \wedge \sim Q) ightarrow(P \wedge Q)$

$\equiv(P \vee Q) \vee(P \wedge Q) 
eq$ Tautology

Aliter:


	
		
			$P$
			$Q$
			$P \vee Q$
			$P \vee Q$
			$\sim P$
			$(P \vee Q) \vee \sim P$
		
		
			$T$
			$T$
			$T$
			$T$
			$F$
			$T$
		
		
			$T$
			$F$
			$T$
			$F$
			$F$
			$T$
		
		
			$F$
			$T$
			$T$
			$F$
			$T$
			$T$
		
		
			$F$
			$F$
			$F$
			$F$
			$T$
			$T$

If $P$ and $Q$ are two statements, then which of the following compound statement is a tautology?

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