---

Contrapositive

Define

The

of the constituents of the conditional

\[\begin{equation*}
  P \implies Q
\end{equation*}
\]

in the form

\[\begin{equation*}
  \lnot Q \implies \lnot P,
\end{equation*}
\]

which, unlike the converse and inverse, is

that is

\[\begin{equation*}
  (P \implies Q) \equiv (\lnot Q \implies \lnot P)
\end{equation*}
\]

For example, the molecular statement, “if you dance, you sweat” is equivalent to “if you do not sweat, you do not dance”.

(Levin, 2021, sec. 0.2)

Example

For example, the statement

“if you are dancing, you are sweating”

is equivalent to

“if you not sweating, you are not dancing”.

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