contradiction

A contradiction involves a proposition conflicting either with itself or established fact.

Aristotle's law of noncontradiction states that

"It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect."

The symbol $\mathrm{\perp }$ (bottom, falsum) represents an arbitrary contradiction.

In propositional logic, it can refer to one of the 16 possible equivalence classes that a truth function can take, e.g. the conjunction of a proposition and its negation:

\documentclass{standalone}
\usepackage{tikz}
%
\definecolor{fillcolor}{HTML}{8A5CF5}
%
\tikzset{truthy/.style n args={1}{%
    fill=#1,draw,%
    inner sep=0,minimum size=1cm}}
%
\begin{document}
\begin{tikzpicture}
	\path (-2,-2) rectangle (2,2);
	\node at (0,0.5) {Contradiction};
	\node at (0,-0.5) {$P\wedge(\neg P)$};
\end{tikzpicture}
\begin{tikzpicture}
	\node at (-1.5,0.5) {$P$};
	\node at (0.5,2.5) {$Q$};
	\node at (-1,0) {\small$1$};
	\node at (-1,1) {\small$0$};
	\node at (0,2) {\small$0$};
	\node at (1,2) {\small$1$};
    \node[truthy={none}] at (0,0) {$0$}; % bottom left
    \node[truthy={none}] at (1,0) {$0$}; % bottom right
    \node[truthy={none}] at (0,1) {$0$}; % top left
    \node[truthy={none}] at (1,1) {$0$}; % top right
\end{tikzpicture}
\hspace{1cm}
\begin{tikzpicture}
	\path (-3,-2) rectangle (3,2);
	%
    \draw (-1,0) circle (1.5);
    \draw (1,0) circle (1.5);
    \node at (-1.25,0) {$P$};
    \node at (1.25,0) {$Q$};
\end{tikzpicture}
\end{document}

See also:
reductio ad absurdum i.e. proof by contradiction
ex falso quodlibet i.e. principle of explosion