Basic Proposicional Logic Proof

basic_proof.tex

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Five ways to prove $P \implies Q$

\begin{itemize}
\item \textbf{Direct Proof}: $P \implies Q$ 
\item \textbf{Proof by Contrapositive}: $\neg Q \implies \neg P$ 
\item \textbf{Proof by Contradicting Conclusion}: $(P \land \neg Q) \implies Q$ 
\item \textbf{Proof by Contradicting Hypothesis}: $(P \land \neg Q) \implies \neg P$
\item \textbf{Proof by Reduction Ad Absurdum}: $(P \land \neg Q) \implies (R \land \neg R)$
\end{itemize}

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