Conjunction implies Disjunction

Theorem

 * $\vdash \left({p \land q}\right) \implies \left({p \lor q}\right)$

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}$