Which one of the following is NOT equivalent to $p \leftrightarrow q$?

The biconditional statement $p \leftrightarrow q$ is true when $p$ and $q$ have the same truth value (both True or both False).

Let us evaluate each option:

• Option A: $(

eg p \lor q) \land (p \lor eg q) \equiv (p \to q) \land (q \to p) \equiv p \leftrightarrow q$.

• Option B: $(

eg p \lor q) \land (q \to p) \equiv (p \to q) \land (q \to p) \equiv p \leftrightarrow q$.

• Option D: $(

eg p \land eg q) \lor (p \land q)$, which is the standard disjunctive normal form (DNF) of$p \leftrightarrow q$.

• Option C: $(

eg p \land q) \lor (p \land eg q)$, which represents the XOR operation ($p \oplus q$), the exact negation of$p \leftrightarrow q$.

Hence, option C is NOT equivalent to $p \leftrightarrow q$.