A B B A - Vidyadip

Question

$A \rightarrow B$
$\sim B$
$\therefore \sim A$

✓

Answer

Combining the two bases of this argument as a whole, the argument will be as follows:
$(A \rightarrow B)\ \&\ \sim B$
$\therefore \sim A$
Truth Table:

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

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. Out of the total four rows of the truth table, only rows. The base statement in $4$ is the truth $‘T’$ and the result statement in the same row is also the truth $‘T’.$ Hence this argument is standard.

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