This is probably an extremely easy solution, but for some reason is it boggling me. I am very new to Illustrator, and figured I would try make a vector logo of something I designed in Photoshop a while back:
On the right is the original .jpg.
I made 4 Layers for the rings and Middle circle.
I made another 'cut through' wave path with the pen tool.
I want to either separate the top and bottom of each ring into it's own movable layer, or even just deleting a 3px wide stroke out of the middle is sufficient.
I can't seem to figure out where to go after making this pen path - perhaps it's not even the right way. Whenever I try to use any pathfinder options, it doesn't cut things out the way I am intending.
It shows how to mask objects in Illustrator and teaches you basics of compound paths, etc.
Basically to cut the logo "in half", first make it a compound path by selecting the logo and type CTRL+8 (pc) or CMD+8 (mac), or in the menu, Object - Compound Path - Make. Then create a 3pt curve going through your logo and outline that path (object - path - outline stroke) so it is no longer a stroke (it will become a solid). Next select this solid curve and your logo, and in the Pathfinder palette, click the "subtract" button (second from the top left).
Try that and let us know if this was what you were trying to accomplish.