User:Noblesp/sandbox

Definitions
For $$p$$, $$q$$. A condition $$p$$ is a necessary condition for $$q$$ when $$p$$ cannot be true unless $$q$$ is true. Formally:


 * $$p \Leftarrow q$$

A condition $$p$$ is a sufficient condition for $$q$$ when $$p$$ must be true if $$q$$ is true. Formally:


 * $$p \Rightarrow q$$

Therefore, a condition $$p$$ is a necessary and sufficient condition for $$q$$ when it meets both of these criteria Formally:
 * $$(p \Leftarrow q) \land (p \Rightarrow q)$$

or
 * $$p \iff q$$