How to get rid of the bonds between bones? I'm not sure what to call them so I'm just going to call it a bond. I deleted a bone to hope that it'll separate a set of bones from another set of bones.

Now this is happening:



The dotted line is where the bones were but the bones still exist as one set of bones. So if I moved one bone further down, it would still affect the arms even though there are no bones connecting them. 

How do I delete these 'bonds'? 

Thanks in advance!
The dotted lines indicate the parent/child relationship. The child always follows the parent which is why the bone moves as it's parent moves.

The parent setting can be found in the bone's relations panel. Clicking the X will clear the parent linked to the bone. 



You can also clear the parent in the 3Dview using &#9095; AltP ->Clear Parent