Rule of Distribution/Disjunction Distributes over Conjunction/Left Distributive
< Rule of Distribution | Disjunction Distributes over Conjunction(Redirected from Disjunction is Left Distributive over Conjunction)
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Theorem
The disjunction operator is left distributive over the conjunction operator:
Formulation 1
- $p \lor \paren {q \land r} \dashv \vdash \paren {p \lor q} \land \paren {p \lor r}$
Formulation 2
- $\vdash \paren {p \lor \paren {q \land r} } \iff \paren {\paren {p \lor q} \land \paren {p \lor r} }$