Conjunction implies Disjunction

Theorem

 * $\vdash \paren {p \land q} \implies \paren {p \lor q}$

Proof
We apply the Method of Truth Tables.

As can be seen by inspection, the truth values under the main connective is true for all boolean interpretations.


 * $\begin{array}{|ccc|c|ccc|} \hline

(p & \land & q) & \implies & (p & \lor & q) \\ \hline \F & \F & \F & \T & \F & \F & \F \\ \F & \F & \T & \T & \F & \T & \T \\ \T & \F & \F & \T & \T & \T & \F \\ \T & \T & \T & \T & \T & \T & \T \\ \hline \end{array}$