Equivalence using conjunction and negation
Task number: 2779
Can we replace the equivalence \(a \Leftrightarrow b\) with a proposition containing only the negation \(\neg\) and conjunction \(\land\) operators?
Resolution
We use two rules: \(a \Leftrightarrow b \iff (a \land b) \lor (\neg a \land \neg b)\) and
\(a \lor b \iff \neg(\neg a \land \neg b)\) and we get
\(a \Leftrightarrow b \iff \neg(\neg(a \land b) \land \neg(\neg a \land \neg b))\).
