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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
$P\ v (Q\ \&\ R)$
$\sim P$
$\therefore Q\ \&\ R$
✓

Answer

Combining the two bases of this argument as a whole, the argument will be as follows:
$[P\ v\ (Q\ \&\ R)]\ \&\ \sim P$
$\therefore Q\ \&\ R$
Truth Table:
  Support Statement The resulting statement
  $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$
$P$ $Q$ $R$ $\sim P$ $Q\ \&\ R$ $P\ v\ (Q\ \&\ R)$ $[P\ v\ (Q\ \&\ R)]\ \& \sim P$ $Q\ \&\ R$
$1$ $T$ $T$ $T$ $F$ $T$ $T$ $F$ $T$
$2$ $T$ $T$ $F$ $F$ $F$ $T$ $F$ $F$
$3$ $T$ $F$ $T$ $F$ $F$ $T$ $F$ $F$
$4$ $T$ $F$ $F$ $F$ $F$ $T$ $F$ $F$
$5$ $F$ $T$ $T$ $T$ $T$ $T$ $T^*$ $T^*$
$6$ $F$ $T$ $F$ $T$ $F$ $F$ $F$ $F$
$7$ $F$ $F$ $T$ $T$ $F$ $F$ $F$ $F$
$8$ $F$ $F$ $F$ $T$ $F$ $F$ $F$ $F$
  $1 (\sim )$ $2,3 (\&)$ $1, 5 (v)$ $6, 4 (\&)$ 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. Out of a total of eight rows of the truth table, only rows. The base statement in $5$ 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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