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, .
Proof. Let be an arbitrary element of . Then and ; hence, . So, .
Conversely, if is arbitrary, then and ; hence, . Thus, .
On the top write in the last set itself
You listed Lara Alcock’s book, but misspelled her name as Laura in the link. Thanks for the recommendation though :)
Should “A \cap A \subseteq A” on the second proof be reversed?