biconditionals and tautologies Is a biconditional necessarily a tautology? For instance, in the proposition (K--->N) iff (N--->K), "iff" is a type of equivalence, correct? So, if a tautology is also an equivalence, then this statement would be tautologous, would it not?

A biconditional, say, $K \longleftrightarrow N\equiv (K \rightarrow N) \land (N\rightarrow K)$ is true only when both $K$ and $N$ are true, or when both $K$ and $N$ are false.

However if one is true and the other false, the biconditional is not true. Hence, it is not true for all truth-value assignments for $K, N$. Hence, it is not a tautology.

We do have that $K \iff N \equiv (K\; \text{ XNor } N)$ and shares the following truth-table:

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