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The forms of the statement and its types — Philosophy STD 12 Arts — Question

Gujarat BoardEnglish MediumSTD 12 ArtsPhilosophyThe forms of the statement and its types3 Marks
Question
$p \rightarrow [q\ \&\ (p \rightarrow r)]$
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Answer

Truth table:
  $1$ $2$ $3$ $4$ $5$ $6$
$p$ $q$ $r$ $p \rightarrow r$ $q\ \&\ (p \rightarrow r)$ $p \rightarrow [q\ \&\ (p \rightarrow r)]$
$1$ $T$ $T$ $T$ $T$ $T$ $T$
$2$ $T$ $T$ $F$ $F$ $F$ $F$
$3$ $T$ $F$ $T$ $T$ $F$ $F$
$4$ $T$ $F$ $F$ $F$ $F$ $F$
$5$ $F$ $T$ $T$ $T$ $T$ $T$
$6$ $F$ $T$ $F$ $T$ $T$ $T$
$7$ $F$ $F$ $T$ $T$ $F$ $T$
$8$ $F$ $F$ $F$ $T$ $F$ $T$
  $1, 3 (\rightarrow)$ $2, 4 (\&)$ $1, 5 (\rightarrow)$
Decision of the type of form for the statement: Looking at the truth table above, it will be seen that the representation of the given form for the statement is in column no. Done in $6.$ Looking at all the rows in this column, it will be clear that it has $‘F’$ in the second, third and fourth rows and $‘T’$ in the first, fifth, sixth, seventh and eighth rows. This means that some of the substitutions of this form for the statement are true, while some of the substitutions are untrue. So it is clear that this form of statement is 'parayat'.

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