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

Question

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

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Answer

Truth table:

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

Decision of the type of form for the statement: Looking at the truth table above, it will be seen that the representation of the given form for the statement is in column no. Done in $6.$ Looking at all the rows in this column, it is clear that it has $‘F’$ in the first, second and fourth rows and $‘T’$ in the third row. This means that some of the substitutions of this form for the statement are true, while some of the substitutions are untrue. So it is clear that this form of statement is 'parayat'.

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