How to solve the following problem - A ∩ B ⊂ A ⊂ A ∪ B?
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
76192
Intersection of volumes defined by inequalities
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
54719
How to handle equality constraints in this problem?
150608
problem on intersecting circles
10839
Problem in Cardinality and Order
13132
If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$)
66563
Is $ (A∪B)×(C∩D)=(A∪C)×(B∪D)$ true for all sets A,B,C and D?
13415
How to show if $A \subseteq B$, then $A \cap B = A$?
130156
Image of the union and intersection of sets.
141101
Russia (2000) contest:Prove the existence of a pair of rows and columns with intersections differently coloured
24685
Expressing a Countable Union of Sets as the Countable Union of Disjoint Sets (e.g. Eliminating Duplicate Intersections)
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
115625
Intersection of two open dense sets is dense
34334
Combinatorics Problem with symbols and spaces
2978
A and B disjoint, A compact, and B closed implies there is positive distance between both sets
64320
Prove that if $0<a<Pr(A)$ then there exists $B\subset A$ such that $Pr(B)=a$