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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:
$P \rightarrow (Q \rightarrow R)$
$\sim R$
$\therefore Q \rightarrow \sim P$
✓

Answer

Combining the two bases of this argument as a whole, the argument will be as follows:
$[P \rightarrow (Q \rightarrow R)] \&\ \sim R$
$\therefore Q \rightarrow \sim P$
Truth Table:
  Support Statement The resulting statement
  $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$
$P$ $Q$ $R$ $\sim P$ $\sim R$ $Q \rightarrow R$ $P \rightarrow (Q \rightarrow R)$ $[P \rightarrow (Q \rightarrow R)]\ \&\ \sim R$ $Q \rightarrow \sim P$
$1$ $T$ $T$ $T$ $F$ $F$ $T$ $T$ $F$ $F$
$2$ $T$ $T$ $F$ $F$ $T$ $F$ $F$ $F$ $F$
$3$ $T$ $F$ $T$ $F$ $F$ $T$ $T$ $F$ $T$
$4$ $T$ $F$ $F$ $F$ $T$ $T$ $T$ $T^*$ $T^*$
$5$ $F$ $T$ $T$ $T$ $F$ $T$ $T$ $F$ $T$
$6$ $F$ $T$ $F$ $T$ $T$ $F$ $T$ $T^*$ $T^*$
$7$ $F$ $F$ $T$ $T$ $F$ $T$ $T$ $F$ $T$
$8$ $F$ $F$ $F$ $T$ $
$		 $T$ $T$ $T^*$ $T^*$
  $1(\sim )$ $3(\sim )$ $2, 3(\rightarrow)$ $1, 6(\rightarrow)$ $7, 5(\&)$ $2, 4(\rightarrow)$
Judgment of the validity of the argument: A total of nine columns have been formed in the above fact sheet. In which the column no.$ 8th$ base statement and column no.$ 9$ is the introduction of the result statement. Row out of the total eight rows of the truth table. The base statement in $4, 6$ and $8$ is the truth $‘T’$ and all the resulting statements in the same row are also the truth $‘T’.$ Hence this argument is standard.

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