Prove that and .

*Proof.*Let be an arbitrary element of . Then or ; hence, . Thus, .

Conversely, if is an arbitrary element of then since it is in . Thus, .

Therefore,

* Proof. * Let be an arbitrary element of . Then and ; hence, . So, .

Conversely, if is arbitrary, then and ; hence, . Thus, .

Therefore,

On the top write in the last set itself

Hi there,

You listed Lara Alcock’s book, but misspelled her name as Laura in the link. Thanks for the recommendation though :)

Hey Rori,

Should “A \cap A \subseteq A” on the second proof be reversed?

Best,

David