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The Law of the Contrapositive.

      

Theorem tex2html_deferredI.3.3       

\fbox{$(p \Rightarrow q) \Longleftrightarrow (\overline{q} \Rightarrow \overline{p})$ }


\begin{proof}\quad
\par\begin{center}
\begin{tabular}{\vert c\vert c\vert c\vert...
...arrow (\overline{q} \Rightarrow \overline{p})$\space as a tautology.
\end{proof}

Very often, it will be impossible to prove a theorem by a direct proof, but the proof via a contrapositive argument will be simple (for example, v.i.  def inj).



Thierry Dana-Picard
2001-10-22