Rule of Distribution/Conjunction Distributes over Disjunction
< Rule of Distribution(Redirected from Conjunction Distributes over Disjunction)
Jump to navigation
Jump to search
Theorem
Conjunction distributes over disjunction:
Conjunction is Left Distributive over Disjunction
Formulation 1
- $p \land \paren {q \lor r} \dashv \vdash \paren {p \land q} \lor \paren {p \land r}$
Formulation 2
- $\vdash \paren {p \land \paren {q \lor r} } \iff \paren {\paren {p \land q} \lor \paren {p \land r} }$
Conjunction is Right Distributive over Disjunction
Formulation 1
- $\paren {q \lor r} \land p \dashv \vdash \paren {q \land p} \lor \paren {r \land p}$
Formulation 2
- $\vdash \paren {\paren {q \lor r} \land p} \iff \paren {\paren {q \land p} \lor \paren {r \land p} }$