If \(x\) is a proposition, then the equivalence \(x\Leftrightarrow \neg x\) is a contradiction (i.e. always invalid).
\(\text{"Socrates is a philosopher if and only if Socrates is not a philosopher"}\) is invalid.
\(a= 2\Leftrightarrow a\neq 2\) is invalid.
Proofs: 1