Proof Writing · Medium problem

If $f$ is not continuous at $a$, then $f$ is not differentiable at $a$.

If $f$ is not differentiable at $a$, then $f$ is not continuous at $a$.

$f$ is differentiable at $a$ and $f$ is not continuous at $a$.

If $f$ is continuous at $a$, then $f$ is differentiable at $a$.