Modus Tollendo Ponens/Variant/Formulation 1/Proof by Truth Table
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Theorem
- $p \lor q \dashv \vdash \neg p \implies q$
Proof
We apply the Method of Truth Tables.
As can be seen by inspection, the truth values under the main connectives match for all boolean interpretations.
$\begin{array}{|ccc||cccc|} \hline p & \lor & q & \neg & p & \implies & q \\ \hline \F & \F & \F & \T & \F & \F & \F \\ \F & \T & \T & \T & \F & \T & \T \\ \T & \T & \F & \F & \T & \T & \F \\ \T & \T & \T & \F & \T & \T & \T \\ \hline \end{array}$
$\blacksquare$
Sources
- 2000: Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems: $\S 1.4.1$: Exercise $1.8: \ 1$