2. If and only if

Sometimes two statements are true or false together. We express this by a double arrow or by the words ``if and only if''.

For any number $x$, $x \geq 0 \Leftrightarrow x^3 \geq 0$.

An additional way to say this is that $x \geq 0$ is a necessary and sufficient condition for $x^3 \geq 0$. Still another way is to say the two statements are equivalent.

The words ``if and only if'' are sometimes abbreviated ``iff''.

Problem B-4. In Problem B-, say which pairs of statements (if any) are equivalent.