# Biconditional as Disjunction of Conjunctions

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## Theorem

#### Formulation 1

- $p \iff q \dashv \vdash \paren {p \land q} \lor \paren {\neg p \land \neg q}$

#### Formulation 2

- $\vdash \paren {p \iff q} \iff \paren {\paren {p \land q} \lor \paren {\neg p \land \neg q} }$

## Also known as

This rule is also sometimes included as another form of the Rule of Material Equivalence