$|A|=|A\cup B|$, where A infinite and B countable
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
127242
$|A\times B|= \text{max}(|A|,|B|)$ for infinite sets
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
132868
Bijection between an infinite set and its union of a countably infinite set
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
48797
Proving Two Sets are Equal - Infinite Sets - Example
6210
Countable compact spaces as ordinals
9021
An infinite subset of a countable set is countable
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
100333
Show A is countable infinity
116527
Validating a proof for necessary and sufficient conditions on sets A & B such that $P(A) \cup P(B) = P(A\cup B)$
95800
Prove that if $\mathcal P(A) \cup \mathcal P(B)= \mathcal P(A\cup B)$ then either $A \subseteq B$ or $B \subseteq A$.
151852
How to prove $A \subset B \iff A \cup B = B$
97697
Countable union of sets of cardinality $c$ has cardinality $c$
99478
countably infinite union of countably infinite sets is countable
67709
Stuck with proof for $\forall A\forall B(\mathcal{P}(A)\cup\mathcal{P}(B)=\mathcal{P}(A\cup B)\rightarrow A\subseteq B \vee B\subseteq A)$
18223
Prove that the union of two disjoint countable sets is countable