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
q is an
antecedent and
p is a
consequent. This is often abbreviated
p iff q. The operator is denoted using a doubleheaded arrow (↔), a prefixed E (E
pq), 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".