left(p^{wedge} rright) Leftrightarrowleft(p^{ | vedclass

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Question

Given $\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right) \equiv(\sim p)$

Taking $r = q$


	
		
			$p$
			$q$
			$\sim

Vedclass · Accepted Answer

$q$

Vedclass · Answer

Given $\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right) \equiv(\sim p)$

Taking $r = q$


	
		
			$p$
			$q$
			$\sim\,p$
			$\sim\,q$
			$p ^{\wedge} q$
			$p ^{\wedge} q$
			$\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right)$
		
		
			$T$
			$T$
			$F$
			$F$
			$T$
			$F$
			$F$
		
		
			$T$
			$F$
			$F$
			$T$
			$F$
			$T$
			$F$
		
		
			$F$
			$T$
			$T$
			$F$
			$F$
			$F$
			$T$
		
		
			$F$
			$F$
			$T$
			$T$
			$F$
			$F$
			$T$
		
	


So, clear $\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right) \equiv(\sim p)$

$\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right)$ is equivalent to $(\sim p)$ when $r$ is.

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