Use truth tables to establish whether the following arguments are valid. If any arguments are invalid, state counterexamples to them. If any arguments are valid, explain carefully using the truth tables why they are valid.
\begin{enumerate}
\item
\begin{equation*}
\begin{fitch}
\fh P \to Q \\
\fa \lnot P \lor Q \\
\end{fitch}
\end{equation*}
\item
\begin{equation*}
\begin{fitch}
\fh P ↔ (Q \to Q) \\
\fa P \lor Q \\
\end{fitch}
\end{equation*}
\item
\begin{equation*}
\begin{fitch}
\fh P \lor \lnot(Q \land R) \\
\fa P \lor (\lnot Q \land R) \\
\end{fitch}
\end{equation*}
\end{enumerate}
