theorem Let A be a set. Then ∪P(A)=A
87830
Relating the union of the power set of a set to the set itself
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
106434
Prove that for a dense set $A$ and an open set $U$, $U\subset \overline{A\cap U}$
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
23764
Proving that $A+A \not\subset 2A $ using a particular definition for sum of sets
153934
How to prove that a set R\Z is open
10909
$|A \cup B| = \mathfrak{c}$, then $A$ or $B$ has cardinality $\mathfrak{c}$.
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
88904
Help with a proof. Countable sets.
13415
How to show if $A \subseteq B$, then $A \cap B = A$?
32441
How to prove or disprove statements about sets
47680
Prove that the union of the interior of a set and the boundary of the set is the closure of the set
99633
Let $α$ be an ordinal and $A$ be a set of ordinals. Then $\sup\limits_{β∈A} (α+β) = α+\sup\limits_{β∈A}(β)$
46056
If $\mathcal{E}$ are subsets of $X$ and $A \subset X$. Show that $\mathcal{A}\mathcal{(E \cap}$ A)=$\mathcal{A}\mathcal{(E)} \cap$ A
94825
Open set as a finite union of closed sets
28223
Prove/Disprove that if two sets have the same power set then they are the same set