Clavius's Law/Formulation 2/Proof by Truth Table
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Theorem
- $\vdash \left({\neg p \implies p}\right) \implies p$
Proof
We apply the Method of Truth Tables.
As can be seen by inspection, the truth value under the main connective is true for all boolean interpretations.
- $\begin{array}{|cccc|c|c|} \hline
(\neg & p & \implies & p) & \implies & p \\ \hline \T & \F & \F & \F & \T & \F \\ \F & \T & \T & \T & \T & \T \\ \hline \end{array}$
$\blacksquare$
Source of Name
This entry was named for Christopher Clavius.
Sources
- 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S \text{II}$: Exercise $13$