True or false?

The best way to reason through something like this is to substitute categories of real things and see if it works. For example,

If all Alakazams are Open Sesame, and some Hocus Pocus are Alakazams, is it true that some Hocus Pocus are Open Sesame?

might become...

If all dogs are animals, and some four-legged animals are dogs, is it true that some four-legged animals are animals?

where

Alakazams = dogs
Open Sesame = animals
Hocus Pocus = four-legged animals

The answer is "yes" with the understanding that "some" does not imply "not all," that is, some can also be all (see http://www.thefreedictionary.com/some )