Modus Tollendo Ponens/Sequent Form/Case 1/Proof by Truth Table

Theorem

 * $p \lor q, \neg p \vdash q$

Proof
We apply the Method of Truth Tables to the proposition.

$\begin{array}{|ccc|cc||c|} \hline p & \lor & q & \neg & p & q\\ \hline F & F & F & T & F & F \\ F & T & T & T & F & T \\ T & T & F & F & T & F \\ T & T & T & F & T & T \\ \hline \end{array}$

As can be seen, when $p \lor q$ is true, and so is $\neg p$, then $q$ is also true.