p & (q r) - Vidyadip

Question

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

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Answer

Truth table:

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

Determining the type of form for a statement: Looking at the truth table above, it will be seen that the representation of the given form for a statement is not a column. Done in $5.$ Looking at all the rows in this column, it will be clear that it has $‘T’$ in the first, second and fourth rows and $‘F’$ in the second, fifth, sixth, seventh and eighth 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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