Rule of Commutation/Disjunction/Formulation 1/Proof 2
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Theorem
- $p \lor q \dashv \vdash q \lor p$
Proof
We apply the Method of Truth Tables.
As can be seen by inspection, in both cases, the truth values under the main connectives match for all boolean interpretations.
$\begin{array}{|ccc||ccc|} \hline p & \lor & q & q & \lor & p \\ \hline \F & \F & \F & \F & \F & \F \\ \F & \T & \T & \T & \T & \F \\ \T & \T & \F & \F & \T & \T \\ \T & \T & \T & \T & \T & \T \\ \hline \end{array}$
$\blacksquare$
Sources
- 1993: M. Ben-Ari: Mathematical Logic for Computer Science ... (previous) ... (next): Chapter $2$: Propositional Calculus: $\S 2.4$: Logical equivalence and substitution: Theorem $2.4.2$
- 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 2.3$: Theorem $2.28$