Does a cold gem override a fire gem?


Diabloii.Net Member
I have a level 26 amazon in act 2 and would like socket an item with three sockets. I would like to know the following :
- Does a cold gem nullify the effects of a fire gem or vice versa?
I would like to know this because when I see the animation for my character hitting an enemy, I see the cold damage animation but I don't see fire damage. Is it just suppose to look that way with a fire and cold gem?

Thanks in advance. :)