Rule of Distribution/Disjunction Distributes over Conjunction
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Theorem
Disjunction distributes over conjunction:
Disjunction is Left Distributive over Conjunction
Formulation 1
- $p \lor \paren {q \land r} \dashv \vdash \paren {p \lor q} \land \paren {p \lor r}$
Formulation 2
- $\vdash \paren {p \lor \paren {q \land r} } \iff \paren {\paren {p \lor q} \land \paren {p \lor r} }$
Disjunction is Right Distributive over Conjunction
Formulation 1
- $\paren {q \land r} \lor p \dashv \vdash \paren {q \lor p} \land \paren {r \lor p}$
Formulation 2
- $\vdash \paren {\paren {q \land r} \lor p} \iff \paren {\paren {q \lor p} \land \paren {r \lor p} }$