A) a fallacy
B) a tautology
C) equivalent to \[\tilde{\ }p\to q\]
D) equivalent to \[p\to -q\]
Correct Answer: B
Solution :
\[(p\to q)[(\tilde{\ }p\to q)\to q]\] \[\left| \begin{align} & p \\ & T \\ & T \\ & F \\ & F \\ \end{align} \right|\left| \begin{align} & q \\ & F \\ & T \\ & F \\ & T \\ \end{align} \right|\left| \begin{align} & \tilde{\ }p \\ & F \\ & F \\ & T \\ & T \\ \end{align} \right|\left| \begin{align} & p\to q \\ & F \\ & T \\ & T \\ & T \\ \end{align} \right|\left| \begin{align} & \tilde{\ }p\to q \\ & T \\ & T \\ & F \\ & T \\ \end{align} \right|\left| \begin{align} & (\tilde{\ }p\to q)\to q \\ & F \\ & T \\ & T \\ & T \\ \end{align} \right|\left| \begin{align} & (p\to q)\to ((\tilde{\ }p\to q)\to q) \\ & T \\ & T \\ & T \\ & T \\ \end{align} \right|\]\[\therefore \] It is tautology
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