If werewolves exist do vampires exist too?

Just a question I thought I’d pose.  I think the clear answer here is no.  Werewolves are living creatures. They die. They are not supernatural, although they may possess more strength and perhaps longer life than normal people or animals, they are still nonetheless mortal. Vampires however - in every legend, story, and myth - are always immortal - they are said to live forever and only sunlight kills them.  This goes against all the laws of nature.  So I think the clear answer to the question is that yes, it is possible for werewolves to exist, but no, not necessarily for vampires to exist too.