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Type the correct answer in each box. Use T for true and F for false.

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

Sagot :

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

Here's the complete truth table:

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