Let r in{p, q, sim p, sim q} be such that the | vedclass

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Question

By options

$(1)$


	
		
			$p = r$
			$q$
			$\sim p$
			$r \vee(\sim p )$
			$( p \wedge q )$
			$( p \wedge q ) \vee r$
			$r \vee(\si

Vedclass · Accepted Answer

$\sim p$

Vedclass · Answer

By options

$(1)$


	
		
			$p = r$
			$q$
			$\sim p$
			$r \vee(\sim p )$
			$( p \wedge q )$
			$( p \wedge q ) \vee r$
			$r \vee(\sim P )\;\Rightarrow \;( p \wedge q ) \vee r$
		
		
			$T$
			$F$
			$F$
			$T$
			$F$
			$T$
			$T$
		
		
			$F$
			$T$
			$T$
			$T$
			$F$
			$F$
			$F$
		
		
			$T$
			$T$
			$F$
			$T$
			$T$
			$T$
			$T$
		
		
			$F$
			$F$
			$T$
			$T$
			$F$
			$F$
			
			$T$
			
		
	


$(2)$


	
		
			$p$
			$\sim p$
			$r \vee(\sim p )$
			$q = r$
			$( p \wedge q )$
			$( p \wedge q ) \vee r$
			$r \vee(\sim p ) \;\Rightarrow\;( p \wedge q ) \vee r$
		
		
			$T$
			$F$
			$T$
			$T$
			$T$
			$T$
			$T$
		
		
			$F$
			$T$
			$T$
			$T$
			$F$
			$T$
			$T$
		
		
			$T$
			$F$
			$F$
			$F$
			$F$
			$F$
			$T$
		
		
			$F$
			$T$
			$T$
			$F$
			$F$
			$F$
			$F$
		
	


$(3)$


	
		
			$p$
			$q$
			$r =\sim p$
			$r \vee(\sim p )$
			$( p \wedge q )$
			$( p \wedge q ) \vee r$
			$r \vee(\sim p ) \;\Rightarrow\;( p \wedge q ) \vee r$
		
		
			$T$
			$T$
			$F$
			$F$
			$T$
			$T$
			$T$
		
		
			$F$
			$T$
			$T$
			$T$
			$F$
			$T$
			$T$
		
		
			$T$
			$F$
			$F$
			$F$
			$F$
			$F$
			$T$
		
		
			$F$
			$F$
			$T$
			$T$
			$F$
			$T$
			$T$
		
	


$(4)$


	
		
			$\sim p$
			$p$
			$q$
			$r \vee(\sim p )$
			$r =\sim p$
			$( p \wedge q )$
			$( p \wedge q ) \vee r$
			$r \vee(\sim p ) \;\Rightarrow\;( p \wedge q ) \vee r$
		
		
			$F$
			$T$
			$T$
			$F$
			$F$
			$T$
			$T$
			$T$
		
		
			$F$
			$T$
			$F$
			$T$
			$T$
			$F$
			$T$
			$T$
		
		
			$T$
			$F$
			$T$
			$T$
			$F$
			$F$
			$F$
			$F$
		
		
			$T$
			$F$
			$F$
			$T$
			$T$
			$F$
			$T$
			$T$
		
	


Now finak answer in option no. $3$

Let $r \in\{p, q, \sim p, \sim q\}$ be such that the logical statement $r \vee(\sim p) \Rightarrow(p \wedge q) \vee r \quad$ is a tautology. Then ' $r$ ' is equal to

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