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