If I see you while you are eating cabbage, then yes, I do expect to see cabbage.

But I think I get it now: There might be multiple suppliers for the same parts, and so supplier 1 might supply screws for project 1, while supplier 2 supplies screws for project 2. In that case, the suppliers <-> projects relation is not the natural composition., while the "connection trap" would suggest that both suppliers supply both projects.