Here's how I would do this. I would create a segment that has email contacts that are both in Group A and Group B. Then I would send the email to this segment.
Not sure I understand when you say 'I would like to see if there is a way to use the lists as an "OR" function.' What you described is an 'AND function': the contacts have to be in Group A AND Group B, right? If you use 'OR', you will have all of the contacts from both groups. Does that help?