Rule of Simplification/Sequent Form/Formulation 1/Form 2

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Theorem

$p \land q \vdash q$


Proof 1

By the tableau method of natural deduction:

$p \land q \vdash q$
Line Pool Formula Rule Depends upon Notes
1 1 $p \land q$ Premise (None)
2 1 $q$ Rule of Simplification: $\land \mathcal E_2$ 1

$\blacksquare$


Proof 2

We apply the Method of Truth Tables.

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

As can be seen, when $p \land q$ is true so is $q$.

$\blacksquare$


Sources