Logical biconditional ($P\leftrightarrow Q$)

A binary logical connective true exactly when its two arguments have the same truth value. It is logically equivalent to $(P\to Q)\wedge (Q\to P)$, and hence to $(\neg P\vee Q)\wedge (\neg Q\vee P)$. Its truth table has value one on input pairs $(0,0)$ and $(1,1)$, and zero on $(0,1)$ and $(1,0)$.