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Complete the truth table for the inverse of a conditional statement.

\begin{tabular}{|c||c||c|c|}
\hline [tex]$p$[/tex] & [tex]$q$[/tex] & [tex]$p \rightarrow q$[/tex] & [tex]$\sim p \rightarrow \sim q$[/tex] \\
\hline \hline [tex]$T$[/tex] & [tex]$T$[/tex] & [tex]$T$[/tex] & [tex]$\square$[/tex] \\
\hline \hline [tex]$T$[/tex] & [tex]$F$[/tex] & [tex]$F$[/tex] & [tex]$\square$[/tex] \\
\hline \hline [tex]$F$[/tex] & [tex]$T$[/tex] & [tex]$T$[/tex] & [tex]$\square$[/tex] \\
\hline \hline [tex]$F$[/tex] & [tex]$F$[/tex] & [tex]$T$[/tex] & [tex]$\square$[/tex] \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
To complete the truth table for the inverse of a conditional statement, we need to determine the values for [tex]\(\neg p \rightarrow \neg q\)[/tex] for each combination of [tex]\(p\)[/tex] and [tex]\(q\)[/tex].

\begin{tabular}{|c||c||c|c|}
\hline [tex]$p$[/tex] & [tex]$q$[/tex] & [tex]$p \rightarrow q$[/tex] & [tex]$\sim p \rightarrow \sim q$[/tex] \\
\hline \hline [tex]$T$[/tex] & [tex]$T$[/tex] & [tex]$T$[/tex] & F \\
\hline \hline [tex]$T$[/tex] & [tex]$F$[/tex] & [tex]$F$[/tex] & T \\
\hline \hline [tex]$F$[/tex] & [tex]$T$[/tex] & [tex]$T$[/tex] & T \\
\hline \hline [tex]$F$[/tex] & [tex]$F$[/tex] & [tex]$T$[/tex] & T \\
\hline
\end{tabular}
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