Do we need axiom of choice to prove $A \subset B \subset A \Rightarrow A = B$
27025
How do I choose an element from a non-empty set?
155207
Confusion regarding one formulation of the Axiom of Choice.
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
93040
$f$ is surjective iff it has a right inverse: using the axiom of choice and errors in ProofWiki
131889
Axiom of choice and calculus
134319
When induction proofs need a choice function
33563
Is the axiom of choice used in the proof that every open set is the union of basis elements (Mukres, Lemma 13.1)
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
83996
For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$
63267
Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$
34045
3 Statements of axiom of choice are equivalent
132287
Axiom of Choice and Right Inverse
142219
Does the splitting lemma hold without the axiom of choice?
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
116527
Validating a proof for necessary and sufficient conditions on sets A & B such that $P(A) \cup P(B) = P(A\cup B)$
64320
Prove that if $0<a<Pr(A)$ then there exists $B\subset A$ such that $Pr(B)=a$
118239
If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$