How to prove the following: Assume A infinite,B denumerable show that A~$A\cup B$
23442
Cardinality of the union of infinite and countable sets
95244
Prove that a finite union of closed sets is also closed
142993
Proof of A ⊆ C and B ⊆ C ⇔ A ∪ B ⊆ C
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
26302
Prove that $(X \cap Y) \cup Z = (X \cup Z) \cap (Y \cup Z)$
117781
Proving that $S=\{\frac{1}{n}:n\in\mathbb{Z}\}\cup\{0\}$ is compact using the open cover definition
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
152817
Proving $\sup B=\inf A$
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
30770
Prove that $C\left(\bigcup_{\alpha\in I} A_\alpha\right)=\bigcap_{\alpha\in I}C\left(A_\alpha\right)$
72190
Topological proof on discrete topology where $X$ is infinite
32965
Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
66398
Union of a finite set and a countably infinite set is countably infinite
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
109070
Question about the proof of the distributive property for sets
151928
How to prove that $N\setminus A$ is finite?
158189
If $\{E_\alpha\}$ is connected, $\bigcap\limits_{\alpha\in A}E \neq \emptyset$, then $\bigcup\limits_{\alpha\in A}E$ is connected