The exponential measure is absolutely continuous w.r.t. Lebesgue measure, never the reverse

Let R be the set of real numbers, B the Borel $\sigma$-field. Let `m' denotes the Lebesgue measure and $\mu$ the measure defined by the function $F(x)=(1-e^{-x})$ if $x>0$ and $F(x)=0$ elsewhere. Consider the statements: (I) $\mu\ll m$, (i.e.
$\mu$ is absolutely continuous w.r.t. $m$). (II) $m\ll\mu$. (III) $\dfrac{d\mu}{dm}(x)=e^{-x} x>0, \dfrac{d\mu}{dm}(x)=0, x\le0$. Which of the above are true?