(p v q) ( p & q) - Vidyadip

Question

$\sim (p\ v\ q) \rightarrow (\sim\ p\ \&\sim\ q)$

✓

Answer

Truth table:

	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
	$p$	$q$	$\sim p$	$\sim q$	$p\ v\ q$	$\sim (p\ v\ q)$	$\sim p\ \& \sim q$	$\sim (p\ v\ q) \rightarrow (\sim\ p \& \sim\ q)$
$1$	$T$	$T$	$F$	$F$	$T$	$F$	$F$	$T$
$2$	$T$	$F$	$F$	$T$	$T$	$F$	$F$	$T$
$3$	$F$	$T$	$T$	$F$	$T$	$F$	$F$	$T$
$4$	$F$	$F$	$T$	$T$	$F$	$T$	$T$	$T$
			$1 (\sim )$	$2(\sim )$	$1, 2(V)$	$5 (\sim )$	$3, 4 (\&)$	$6, 7 (\rightarrow)$

Decision of the type of form for the statement: Looking at the fact sheet above, it will be seen that the representation of the given form for the statement is in column no. All the rows of this column in $8$ have $‘T’$ in them. This means that all substitutions for this form of statement are true. So it is clear that this form of statement is 'tadevarthaka'.

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