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:
$R \rightarrow (S\ v\ T)$
$\sim R$
$\therefore S\ v\ T$

✓

Answer

Combining the two bases of this argument as a whole, the argument will be as follows:

$[R \rightarrow (S\ v\ T)]\ \&\ \sim\ R$
$\therefore S\ v\ T$
Truth Table:

							Support Statement	The resulting statement
	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
	$R$	$S$	$T$	$\sim R$	$S\ v\ T$	$\rightarrow (S\ v\ T)$	$[R \rightarrow (S\ v\ T)]\ \&\ \sim R$	$S\ v\ T$
$1$	$T$	$T$	$T$	$F$	$T$	$T$	$F$	$T$
$2$	$T$	$T$	$F$	$F$	$T$	$T$	$F$	$T$
$3$	$T$	$F$	$T$	$F$	$T$	$T$	$F$	$T$
$4$	$T$	$F$	$F$	$F$	$F$	$F$	$F$	$F$
$5$	$F$	$T$	$T$	$T$	$T$	$T$	$T$	$T$
$6$	$F$	$T$	$F$	$T$	$T$	$T$	$T$	$T$
$7$	$F$	$F$	$T$	$T$	$T$	$T$	$T$	$T$
$8$	$F$	$F$	$F$	$T$	$F$	$T$	$T^*$	$F^*$
				$1(\sim )$	$2, 3(v)$	$1, 5(\rightarrow)$	$6, 4(\&)$	AS $5$

Judgment of the validity of the argument: A total of eight columns have been formed in the above fact sheet. In which the column no. $7th$ base statement and column no. $8$ is the introduction of the result statement. Row out of the total eight rows of the truth table. The base statement in $5, 6, 7$ and $8$ is true $‘T’$ but not row. The result statement in $8 $ is false $‘F’.$ Hence this argument is disproportionate.

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