Contradiction Rule is a valid #Argument which states that if \(p\) is false leads to a contradiction, then \(p\) must be true. This is shown as below:
$$ \begin{align} &\sim p \rightarrow \textbf{c} \\ \therefore \ &p \end{align} $$
It can be proved by the following Truth Table# :
| \(p\) | \(\sim p\) | \(\textbf{c}\) | \(\sim p \rightarrow \textbf{c}\) | \(p\) |
|---|---|---|---|---|
| T | F | F | T | T |
| F | T | F | F |