I've been going through some old exam papers, and I came upon an interesting part of a question that I'm not sure how to solve. Throughout the question I've been proving things like $\displaystyle b\in b$ is false, at most one of $\displaystyle b\in c$ and $\displaystyle c\in b$ is true, and so on. I've been asked whether any of the following can occur, using only axioms (ZF1)-(ZF4) and (ZF9). (Extensionality, null set, pairs, unions, foundation.)

1. $\displaystyle x\in\bigcup x$

2. $\displaystyle x\in\bigcup \bigcup x$

3. $\displaystyle \bigcup x \in x$

I think (1) is false, by extension I think (2) is false (but can't get my reasoning right in my head), and I'm not sure about (3).