Contradiction is Negation of Tautology/Proof by Truth Table

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A contradiction implies and is implied by the negation of a tautology:

$\bot \dashv \vdash \neg \top$

That is, a falsehood can not be true, and a non-truth is a falsehood.


We apply the Method of Truth Tables to the proposition.

As can be seen by inspection, the truth values in the appropriate columns match.

$\begin{array}{|c||cc|} \hline \top & \neg & \bot \\ \hline \T & \T & \F \\ \hline \end{array}$