Visualise Users Group Selection and Intersection

I have a design challenge to simplify the visualisation of user's group permissions with intersections.

The main challenge is to make easy to read by non technical users some complex selections and at the same time make it visually as simple as possible. The expressions would be something like:

The number of groups included in the expression is variable so this can be quite long ...

My current idea is to keep natural language if possible, but this can make expressions really long.