The
of the antecedent and the consequent of the conditional
\[\begin{equation*}
P \implies Q
\end{equation*}
\]
in the form
\[\begin{align*}
& P \impliedby Q \\
\qor & Q \implies P,
\end{align*}
\]
which, unlike the contrapositive, is
so
\[\begin{equation*}
(Q \implies P) \> \not \equiv \> (P \implies Q),
\end{equation*}
\]
but is
so
\[\begin{equation*}
(Q \implies P) \> \equiv \> (\lnot P \implies \lnot Q).
\end{equation*}
\]