(p V q) (p & q) - Vidyadip

Question

$(p\ V\ q) \rightarrow (p\ \&\ q)$

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Answer

Truth table:

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

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. $5,$ looking at all the rows in this column, it is clear that it has $‘F’$ in the second and third rows and $‘T’$ in the first and fourth rows. 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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