JNU SSS 2013 Question 11: Logic and proof techniques

An exclusive club is trying very hard to pick its members from the social elite. An exact election mechanism has been agreed upon that will ensure the entrance of only the most suave members from the group $A$, $B$, $C$, $D$, $E$, $F$, $G$ and $H$. Being ‘in’ or ‘out’ of the club is determined by the following rules : If $A$ is in, then $G$ is out. If $H$ is out, then $B$ is in. If $D$ is out, then $E$ is out. If $H$ is in, then $C$ is in. If $B$ is out, then $G$ and $D$ are out.

If $B$ is out, then who must be in?