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Lemma: A proposition cannot be equivalent to its negation

If \(x\) is a proposition, then the equivalence \(x\Leftrightarrow \neg x\) is a contradiction (i.e. always invalid).

Examples:

\(\text{"Socrates is a philosopher if and only if Socrates is not a philosopher"}\) is invalid.

\(a= 2\Leftrightarrow a\neq 2\) is invalid.

Table of Contents

Proofs: 1

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