If you don't believe something exists, then you believe it doesn't exist. True or false?

False. If something was never known to you until someone mentioned it, then you only know that they believe it exists. You haven't experienced it, so you are not a believer in its existance yet, but you don't have information to confirm that it cannot and does not exist. Such is the dilemma with discussing God, Jesus, Buddha Muhammad, Krishna or whomever. They cannot prove the existance and you cannot prove the diety's non-existance.