Elementary Set theory proof: $A \subseteq B$ iff $A \cap B=A$
49143
Showing $A \subset B \iff A\cap B=A$
41477
Prove $f(S \cap T) \subseteq f(S) \cap f(T)$
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
114599
$A \cup B$ and $A \cap B$ connected $\implies A$ and $B$ are connected
87327
Unions and intersections: $(A \cup B = A ∪ C) \land (A \cap B = A ∩ C) \implies B = C.$
79697
If $A$ is a subset of $B$, then the closure of $A$ is contained in the closure of $B$.
136789
How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?
134071
If A is a finite set and B is an infinite set, then B\A is an infinite set
140668
Union of $2$ set $A, B$ where $ A$ is a subset of $B$
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
134770
For sets $A,B$, $A \cap (B \setminus A) \subseteq \varnothing$
53551
$f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
25553
elementary set theory (cartesian product and symmetric difference proof)
70307
$(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$