- Write down a formula expressing the statement that the set $S$ is a singleton (i.e., $S$ has exactly one element).
- Write down a formula expressing the statement that the set $S$ contains $x$ and $y$ but no other elements.
- Using the axiom of extensionality, show that there is a unique set $S$ that contains $x$ and $y$ but no other elements.
- Prove Proposition 3.1.28 from the text (Analysis I by Terence Tao).