Two statements $A$ and $B$ are said to be logically equivalent (typically shortened to equivalent) when $A$ is true if and only if $B$ is true (that is, $A$ implies $B$ and $B$ implies $A$ . This is usually written as $A \Leftrightarrow B$ For example, for any integer $z$ the statement ``$z$ is positive'' is equivalent to ``$z$ is not negative and $z\neq 0$ '.