Definition:Biconditional

Definition
The biconditional is a binary connective:
 * $p \iff q$

defined as:
 * $\left({p \implies q}\right) \land \left({q \implies p}\right)$

That is:
 * If $p$ is true, then $q$ is true, and if $q$ is true, then $p$ is true.

$p \iff q$ can be voiced:
 * $p$ if and only if $q$.

Also known as
Other names for this operator include:
 * equivalence
 * material equivalence
 * logical equivalence
 * logical equality

Also see

 * Definition:Therefore
 * Definition:Because
 * Definition:Logical Equivalence
 * Definition:Conditional