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The form of the argument and the validity of the argument — Philosophy STD 12 Arts — Question

Gujarat BoardEnglish MediumSTD 12 ArtsPhilosophyThe form of the argument and the validity of the argument3 Marks
Question
Determine the validity of the following arguments using the direct method of truth table:
$P \rightarrow \sim (Q\ \&\ R)$
$\therefore\ \sim (Q\ \&\ R) \rightarrow P$
✓

Answer

 
Truth Table:
  Support Statement The resulting statement
  $1$ $2$ $3$ $4$ $5$ $6$ $7$
$P$ $Q$ $R$ $Q\ \&\ R$ $\sim (Q\ \&\ R)$ $P \rightarrow \sim   (Q\ \&\ R)$ $\sim (Q\ \&\ R) \rightarrow P$
$1$ $T$ $T$ $T$ $T$ $F$ $F$ $T$
$2$ $T$ $T$ $F$ $F$ $T$ $T$ $T$
$3$ $T$ $F$ $T$ $F$ $T$ $T$ $T$
$4$ $T$ $F$ $F$ $F$ $T$ $T$ $T$
$5$ $F$ $T$ $T$ $T$ $F$ $T$ $T$
$6$ $F$ $T$ $F$ $F$ $T$ $T^*$ $F^*$
$7$ $F$ $F$ $T$ $F$ $T$ $T^*$ $F^*$
$8$ $F$ $F$ $F$ $F$ $T$ $T^*$ $F^*$
  $2,3(\&)$ $4(\sim )$ $1, 2(\rightarrow)$ $5,1(\rightarrow)$
Judgment of the validity of the argument: A total of seven columns are formed in the above truth table. In which the column no. $6th$ base statement and column no. $7$ is the introduction of the result statement. Flowers of the table of truth out of eight rows. In $2, 3, 4, 5, 6, 7$ and $8$ the base statement truth is $‘T’.$ But of the row. The result statement in $6, 7$ and $8$ is false $‘F’.$ Hence this argument is disproportionate.

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