Determine the validity of the following arguments using the direc… - Vidyadip

Question

Determine the validity of the following arguments using the direct method of truth table:
$A\ v\ (B\ \&\ C)$
$\sim A$
$\therefore B\ \&\ C$

✓

Answer

Truth Table: Judgment of the validity of the argument:
A total of six columns have been formed in the above fact sheet. In which the column no. Base statement and column no. $6$ is the representation of the result statement. Row out of the total four rows of the truth table. The base statement in $2, 3$ and $4$ is the truth $‘T’$ and all the resulting statements in the same row are also the truth $‘T’.$ Hence this argument is standard.

					Support Statement	The resulting statement
	$1$	$2$	$3$	$4$	$5$	$6$
	$P$	$Q$	$\sim P$	$\sim Q$	$P \rightarrow \sim Q$	$Q \rightarrow \sim P$
$1$	$T$	$T$	$F$	$F$	$F$	$F$
$2$	$T$	$F$	$F$	$T$	$T^*$	$T^*$
$3$	$F$	$T$	$T$	$F$	$T^*$	$T^*$
$4$	$F$	$F$	$T$	$T$	$T^*$	$T^*$
			$1(\sim )$	$2(\sim )$	$1, 4(\rightarrow)$	$2, 3(\rightarrow)$

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