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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
$(P\ v\ Q)\ \&\ \sim\ (P\ v\ Q)$
✓

Answer

Truth table
Column $\rightarrow$ $1$ $2$ $3$ $4$ $5$
Row $\downarrow$ $P$ $Q$ $P v Q$ $\sim (P\ v\ Q)$ $(P\ v\ Q)\ \&\ \sim\ (P\ v\ Q)$
$1$ $T$ $T$ $T$ $F$ $F$
$2$ $T$ $F$ $T$ $F$ $F$
$3$ $F$ $T$ $T$ $F$ $F$
$4$ $F$ $F$ $F$ $T$ $F$
  $1, 2 (v)$ $3(\sim )$ 3, 4 (&)
Explanation: $(P\ v\ Q)\ \&\ \sim (P\ v\ Q)$ is the column no. $1$ and $2$ are the first pillars, while the remaining three are the secondary pillars. Column no. $5$ presents the whole complex joint statement. Column no. The following facts are clear from $5:$
$(1)$ According to the first row, if $P$ is true and $Q$ is true, then $(P\ v\ Q)\ \&\ \sim (P\ v\ Q)$ the whole statement is untrue.
$(2)$ According to the second row if $P$ is true and $Q$ is untrue, then $(P\ v\ Q)\ \&\ \sim\ (P\ v\ Q)$ the whole statement is untrue.
$(3)$ According to the third row, if $P$ is true and $Q$ is true, then $(P\ v\ Q)\ \&\ \sim\ (P\ v\ Q)$ the whole statement is untrue.
$(4)$ According to the fourth row if $P$ is untrue and $A\ Q$ is untrue, then $(P\ v\ Q)\ \&\ \sim\ (P\ v\ Q)$ the whole statement is untrue.

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