To complete the truth table for the inverse of a conditional statement (¬p ➔ ¬q), we fill in the results as follows based on the given information:
[tex]\[
\begin{array}{|c||c||c|c|}
\hline
p & q & p \rightarrow q & \sim p \rightarrow \sim q \\
\hline
T & T & T & \text{F} \\
\hline
T & F & F & \text{T} \\
\hline
F & T & T & \text{T} \\
\hline
F & F & T & \text{T} \\
\hline
\end{array}
\][/tex]
So, we have:
- When [tex]\(p\)[/tex] is T (True) and [tex]\(q\)[/tex] is T (True), [tex]\( ¬p ➔ ¬q \)[/tex] is F (False).
- When [tex]\(p\)[/tex] is T (True) and [tex]\(q\)[/tex] is F (False), [tex]\( ¬p ➔ ¬q \)[/tex] is T (True).
- When [tex]\(p\)[/tex] is F (False) and [tex]\(q\)[/tex] is T (True), [tex]\( ¬p ➔ ¬q \)[/tex] is T (True).
- When [tex]\(p\)[/tex] is F (False) and [tex]\(q\)[/tex] is F (False), [tex]\( ¬p ➔ ¬q \)[/tex] is T (True).
