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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 argument5 Marks
Question
If the student works hard in philosophy, first class will be obtained.
The student will do well in philosophy.
Therefore, the student will receive first class.
✓

Answer

Hint: $P =$ Student will work hard in philosophy.
$Q =$ The student will receive first class.
Symbolic representation of the argument:
$P\rightarrow Q$
$P$
$\therefore Q$
Combining the two bases of this argument as a whole, the argument will be as follows:
$(P\rightarrow Q) \& P$
$\therefore Q$
Truth Table:
  Support Statement The resulting statement
  $1$ $2$ $3$ $4$ $5$
$P$ $Q$ $P\rightarrow Q$ $(P \rightarrow Q) \&  P$ $Q$
$1$ $T$ $T$ $T$ $T^*$ $T^*$
$2$ $T$ $F$ $F$ $F$ $F$
$3$ $F$ $T$ $T$ $F$ $T$
$4$ $F$ $F$ $T$ $F$ $F$
  $1, 2(\rightarrow)$ $3, 1 (\&)$ As $2$
Judgment of the validity of the argument: A total of five columns have been formed in the above fact sheet. In which the column no.$ 4th$ base statement and column no.$ 5$ is the representation of the result statement. Out of the total four rows of the truth table, only rows. The base statement in $1$ is truth $‘T’$ and the resulting statement in the same row is also truth $‘T’$ Hence this argument is standard.

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