Conjunction implies Disjunction/Proof 2

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


By the tableau method of natural deduction:

$\paren {p \land q} \implies \paren {p \lor q} $
Line Pool Formula Rule Depends upon Notes
1 1 $p \land q$ Assumption (None)
2 1 $p$ Rule of Simplification: $\land \EE_1$ 1
3 1 $p \lor q$ Rule of Addition: $\lor \II_1$ 2
4 $\paren {p \land q} \implies \paren {p \lor q}$ Rule of Implication: $\implies \II$ 1 – 3 Assumption 1 has been discharged