If $A$ and $B$ are connected, then $A\cup B$ is connected
23225
Union of connected subsets is connected if intersection is nonempty
133699
Proving that there is a bijection between $A$ and $B$.
106564
Suppose $A,B,C$ are sets. Prove that $A\mathbin\triangle B\subseteq C \iff A\cup C=B\cup C$.
148668
How to show $A\times (B\cup C) = (A\times B)\cup (A\times C)$
111763
True or False $A - C = B - C $ if and only if $A \cup C = B \cup C$
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
108394
Proof of that every interval is connected
140440
Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
44673
$M$ connected $\iff$ $M$ and $\emptyset$ are the only subsets of $M$ open and closed at the same time
123890
Show $A\setminus (A\cap B)=(A\cup B)\setminus B$
116866
$A\times B$ connected component implies $A,B$ connect components
157218
If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
153492
Let $p\colon X \to Y$ be a quotient map then if each set $p^{-1}({y})$ is connected, and if $Y$ is connected, then $X$ is connected.
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
80876
Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
101803
A\(B∩C) = (A\B) ∪ (A\C) how to prove?
36878
Prove that $\operatorname{SL}(n,\Bbb R)$ is connected.