P if and only if Q
The proposition P if and only if Q is true if and only if both P and Q are true, or if both P and Q are false. It is false only when one of them is true and the other false.
|Q||Not P if and only if Q|
The biconditional is a complex operator, built out of simpler operators. Think of it this way:<dl>
The if and only if operator plays a special role in definitions. When we say P if and only if q, we are saying that P says the same thing as Q.