I need this to be white for a water bottle but I can't figure out how to make it work.
And this is what happens when I stroke. I am fairly new to Illustrator and this is really throwing me off
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Here's what I would do.
Select all. Change everything to have a white fill and a black stroke. A thick black stroke:
Object > Expand and then click the OKAY button.
Click the Merge button on the Pathfinder Panel (
Window > Pathfinder not Effect > Pathfinder)
Select a black area and hit the Delete key.
General cleanup: Draw a rectangle with no fill and no stroke and then choose
Select > Same > Fill & Stroke. Then hit the Delete key again to remove these "hollow" shapes.
You then have white art with a gap between shapes to retain the overall visual in one color:
This is merely an auto traced representation of the artwork. Actual native paths may be cleaner overall, resulting in better final artwork.
I hope I understand what you want to achieve....
Select it and apply a White stroke (I did 5pt thick) and set fill to none (/) for all the shapes.
Then use the Shape Builder Tool (Shift+M) - Click+Drag to merge the shapes accordingly (see gif)
It can seem a little more complicated if they overlap more - it is still the same process, you just have to think more and take your time.
You can also do the opposite to have the shapes filled and the strokes clear - see @Scott's answer
Just don't apply the stroke to the circle part itself: