Prove by double inclusion the set identity $A\cap(A\cup B) = A$
74077
A intersection (A union B)
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
46875
The identity morphism in $\mathbf{Set}$ is the identity function
39455
Prove that $(X\times Y)\setminus (A\times B)$ is connected
64586
How to prove that $\neg((A\cap B)\cup (\neg A \cap C)) = (A\cap\neg B)\cup (\neg A\cap \neg C)$
10909
$|A \cup B| = \mathfrak{c}$, then $A$ or $B$ has cardinality $\mathfrak{c}$.
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
68258
Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
101803
A\(B∩C) = (A\B) ∪ (A\C) how to prove?
106756
Union and Intersection of Sets $A_{i}$ and $B_{j}$
45666
de morgan law $A\setminus (B \cap C) = (A\setminus B) \cup (A\setminus C) $
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
49143
Showing $A \subset B \iff A\cap B=A$
13132
If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$)