\documentclass[12pt,a4paper]{article}
\usepackage{german}
\usepackage[utf8]{inputenc}
\usepackage{textcomp}
\usepackage{tabularx}

\begin{document}

\section*{4}
\subsection*{1}
\begin{tabularx}{\textwidth}{c|c|c||c}
$\mathbf{p}$ & $\mathbf{q}$ & $\mathbf{r}$ & $\mathbf{((p \Rightarrow q) \wedge (q \Rightarrow r)) \Rightarrow (q \Leftrightarrow r)}$ \\
%\textbf{p} & \textbf{q} & \textbf{r} & \textbf{((p => q) \^ (q => r)) => (q <=> r)} \\
\hline
$0$ & $0$ & $0$ & $1$ \\
$0$ & $0$ & $1$ & $0$ \\
\hline
$\mathit{0}$ & $\mathit{1}$ & $\mathit{0}$ & $\mathit{1}$ \\
$\mathit{0}$ & $\mathit{1}$ & $\mathit{1}$ & $\mathit{0}$ \\
$\mathit{1}$ & $\mathit{0}$ & $\mathit{0}$ & $\mathit{0}$ \\
$\mathit{1}$ & $\mathit{0}$ & $\mathit{1}$ & $\mathit{0}$ \\
$\mathit{1}$ & $\mathit{1}$ & $\mathit{0}$ & $\mathit{0}$ \\
$\mathit{1}$ & $\mathit{1}$ & $\mathit{1}$ & $\mathit{0}$ \\
\hline
\multicolumn{4}{l}{Tautologie: nein} \\
\end{tabularx}

\section*{4}
\subsection*{2}
\begin{tabularx}{\textwidth}{c|c|c||c}
$\mathbf{p}$ & $\mathbf{q}$ & $\mathbf{r}$ & $\mathbf{((p \Rightarrow q) \wedge (q \Rightarrow r)) \Rightarrow (q \Rightarrow r)}$ \\
%\textbf{p} & \textbf{q} & \textbf{r} & \textbf{((p => q) \^ (q => r)) => (q => r)} \\
\hline
$0$ & $0$ & $0$ & $1$ \\
$0$ & $0$ & $1$ & $1$ \\
$0$ & $1$ & $0$ & $1$ \\
$0$ & $1$ & $1$ & $1$ \\
$1$ & $0$ & $0$ & $0$ \\
\hline
$\mathit{1}$ & $\mathit{0}$ & $\mathit{1}$ & $\mathit{1}$ \\
$\mathit{1}$ & $\mathit{1}$ & $\mathit{0}$ & $\mathit{1}$ \\
$\mathit{1}$ & $\mathit{1}$ & $\mathit{1}$ & $\mathit{1}$ \\
\hline
\multicolumn{4}{l}{Tautologie: nein} \\
\end{tabularx}

\section*{4}
\subsection*{3}
\begin{tabularx}{\textwidth}{c|c|c||c}
$\mathbf{p}$ & $\mathbf{q}$ & $\mathbf{r}$ & $\mathbf{((p \Rightarrow q) \Rightarrow r ) \Rightarrow (p \Rightarrow (q \Rightarrow r))}$ \\
% ((p => q) => r) => (p => (q => r)) %
\hline
$0$ & $0$ & $0$ & $1$ \\
$0$ & $0$ & $1$ & $1$ \\
$0$ & $1$ & $0$ & $1$ \\
$0$ & $1$ & $1$ & $1$ \\
$1$ & $0$ & $0$ & $1$ \\
$1$ & $0$ & $1$ & $1$ \\
$1$ & $1$ & $0$ & $1$ \\
$1$ & $1$ & $1$ & $1$ \\
\hline
\multicolumn{4}{l}{Tautologie: ja} \\
\end{tabularx}

\section*{4}
\subsection*{4}
\begin{tabularx}{\textwidth}{c|c|c||c}
$\mathbf{p}$ & $\mathbf{q}$ & $\mathbf{r}$ & $\mathbf{((p \Rightarrow q) \Rightarrow q) \Rightarrow p}$ \\
% ((p => q) => q) => p %
\hline
$0$ & $0$ & $0$ & $1$ \\
$0$ & $0$ & $1$ & $1$ \\
$0$ & $1$ & $0$ & $1$ \\
$0$ & $1$ & $1$ & $1$ \\
$1$ & $0$ & $0$ & $1$ \\
$1$ & $0$ & $1$ & $1$ \\
$1$ & $1$ & $0$ & $1$ \\
$1$ & $1$ & $1$ & $1$ \\
\hline
\multicolumn{4}{l}{Tautologie: ja} \\
\end{tabularx}

\end{document}