Download App

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:
$\sim P\ v \sim Q$
$Q$
$\therefore \sim P$
✓

Answer

Combining the two bases of this argument as a whole, the argument will be as follows:
$(\sim P\ v \sim Q)\ \&\ Q$
$\therefore \sim P$
Truth Table:
  Support Statement The resulting statement
  $1$ $2$ $3$ $4$ $5$ $6$ $7$
$P$ $Q$ $\sim P$ $\sim Q`$ $\sim P\ v \sim Q$ $(\sim\ P\ v\ \sim\ Q)\ \&\ Q$ $\sim P$
$1$ $T$ $T$ $F$ $F$ $F$ $F$ $F$
$2$ $T$ $F$ $F$ $T$ $T$ $F$ $F$
$3$ $F$ $T$ $T$ $F$ $T$ $T^*$ $T^*$
$4$ $F$ $F$ $T$ $T$ $T$ $F$ $T$
  $1(\sim )$ $2(\sim )$ $3, 4(v)$ $5, 2(\&)$ As $3$
Judgment of the authenticity of the argument: In the above fact sheet, seven full pillars have been formed. In which the column no. $6th$ base statement and column no. $7$ is the presentation of the result statement. Out of the total four rows of the truth table, only row no. The base statement truth in $3$ is $‘T’$ and the resulting statement truth in the same row is $‘T’.$ Hence this argument is standard.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "question To The Point .Marks)" from The form of the argument and the validity of the argument→The form of the argument and the validity of the argument — all question types→Philosophy STD 12 Arts question papers→Gujarat Board STD 12 Arts question papers→Gujarat Board question paper generator→

Similar questions

(p $\rightarrow$ q) $\leftrightarrow$ (~ p $\rightarrow$ ~ q)
→
Prove that the following arguments are standard by constructing metaphorical proof
$A\ \rightarrow\ B$
$(R\ \&\ D)\ v\ A$
$T\ v\ [(R\ \&\ D)\ \rightarrow\ W]$
$D\ \&\ \sim\  T$
$\therefore\ [D\ \&\ (W\ v\ B)])\ v\ \sim\ A$
→
Pratyahara
→
Prove that the following arguments are standard by constructing metaphorical proof
$(A\ \&\ D) \rightarrow C$
$E\rightarrow (B\ v\ D)$
$F \rightarrow (A\ \&\ D)$
$F\ \&\ G$
$C\ v\ (B\ v\ D)$
→
Prove that the following arguments are standard by constructing metaphorical proof
$(A\  \rightarrow\ B)\ v\ D$
$H\  \rightarrow\  [(A \ \rightarrow\  B)\  \rightarrow\  R]$
$D\ \rightarrow\ E$
$(E\ v\ F)\  \rightarrow\ H$
$E\ v\ F$
$(R\ v\ E)\ \&\ H$
→
$(p \rightarrow q)\ v\ (q \rightarrow p)$
→
Prove that the following arguments are standard by constructing metaphorical proof
$(P\ \&\ Q) \rightarrow S$
$S \rightarrow ( \sim L \rightarrow \sim N)$
$\sim L\ \&\ \sim N$
$P\ \&\ Q$
$\therefore\sim N\ v\ F$
→
Prove that the following arguments are standard by constructing metaphorical proof
$\sim (A \ \&\ B) \rightarrow H$
$F\ v \sim (H \ \&\ F)$
$(A \ \&\ B) \rightarrow (H \ \&\ F)$
$\sim F \ \&\ (D \ \&\ E)$
$(D \ \&\ E) \ \&\ H$
→
A$\rightarrow$ ~ B
B
$\therefore$ ~ A
→
Prove that the following arguments are standard by constructing metaphorical proof
$(P\ v\ R)\ \rightarrow (S\ v\ T)$
$\sim M\ \&\ \sim N$
$N\ v \sim (S\ v\ T)$
$H \rightarrow (P\ v\ R)$
$[\sim H\ \&\ \sim (P\ v\ R)]\ v\ S$
→