After studying direct rules for conditionals, conjunctions, and disjunctions, we now consider a different proof strategy. Contradiction and indirect proof show that a statement may be established by proving that its denial leads to an impossible statement. This method is especially useful when a direct route to the conclusion is not visible. In this lesson, contradiction and indirect proof will be connected with valid argument forms and formal proof steps.

A \textbf{contradiction} is a statement that is always false. In textbook notation, a contradiction may be denoted by $F_0$. An example of a contradiction is $$\begin{equation*} p\land\neg p. \end{equation*}$$