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
    \(a \Leftrightarrow b \iff \neg(\neg(a \land b) \land \neg(\neg a \land \neg b))\).

Difficulty level: Moderate task
Proving or derivation task
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