Logical biconditional

In logic and mathematics, the logical biconditional (sometimes known as the material biconditional) is the logical connective of two statements asserting "p if and only if q", where p is an antecedent and q is a consequent. This is often abbreviated p iff q. The operator is denoted using a doubleheaded arrow (↔), a prefixed E (Epq), an equality sign (=), an equivalence sign (≡), or EQV. It is logically equivalent to (p → q) ∧ (q → p), or the XNOR (exclusive nor) boolean operator. It is equivalent to "(not p or q) and (not q or p)". It is also logically equivalent to "(p and q) or (not p and not q)", meaning "both or neither".