I have not come to any conclusive answers on the following after many hours of research on many websites to the specific issue that I am trying to figure out.

My company has two websites a main one at www.example.com and one at subdomain.example.com which is a subdomain of the first and is our self hosted blog. The way Google sees these with the www or no-www (called naked for now on) is that each of these actually are different when the www or naked version is used/not used in the front of the domain. I completely understand this. It is also advised that both should be set up in the Google Webmaster Tools, which I have done. Correct me if I am wrong on that in regard to having both set up.

Now the way it appears is that we can set a preferred domain up in Webmaster Tools only at the root domain level. The subdomain can not have this and actually says the following "Restricted to root level domains only". So it appears that the domain should follow what the root domain says which on our preferred one says to display the www.example.com. and not the naked version. That is one issue I have in that one displays one way and the other displays another. Is it that we have the wrong redirects in place for the subdomain? Another question is does this have any affect on SEO in regards to duplicate content on the web in how we have set this up?