Law of Identity/Formulation 2/Proof by Truth Table
Jump to navigation
Jump to search
Theorem
Every proposition entails itself:
- $\vdash p \implies p$
Proof
We apply the Method of Truth Tables to the proposition.
As can be seen by inspection, the truth value under the main connective is $\T$ throughout.
$\begin{array}{|ccc|} \hline p & \implies & p \\ \hline \F & \T & \F \\ \T & \T & \T \\ \hline \end{array}$
$\blacksquare$
Sources
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $2$: The Propositional Calculus $2$: $3$ Truth-Tables: Exercise $1 \ \text{(i) (a)}$