As Captain of the USS Enterprise, your mission is to travel at warp speed to the planet Zorg to rescue some Vulcans whose vessel recently crashed. But beware Romulan spies may be trying to infiltrate your ship! When you arrive, you find three aliens named Aravik, Balev, Chulak. They offer up the following statements:

Aravik: I am a Vulcan or Balev is a Romulan.

Balev: Aravik is a Vulcan and Chulak is a Romulan.

Chulak: Balev and I are different.

Knowing as you do that Vulcans always tell the truth and Romulans always lie which of the aliens, if any, do you rescue and which do you leave stranded on the planet? In your answer, clearly demonstrate that there is only one possible solution by enumerating all possible combinations of Romulans and Vulcans. Explain why each combination except one cannot be valid either because a Vulcan is lying or a Romulan is telling the truth.