Showing that if $a$ is a transitive set then $\cup a$ is also a transitive set.
122271
A subset of a transitive set is transitive
151676
Being characteristic is transitive
75966
Prove that if $A$ is a set with $m$ elements, $B$ is a set with $n$ elements, and $A \cap B = \emptyset$, then $A \cup B$ has $m+n$ elements.
47056
Show that the boundary of a set equals the boundary of its complement
38946
Show that $\{\cup_{n\in K} (n, n+1]: K \subset \mathbb{Z}\}$ is a $\sigma$-algebra on $\mathbb{R}$
2287
If a set is linearly independent, a finite subset of that set is also linearly independent
123890
Show $A\setminus (A\cap B)=(A\cup B)\setminus B$
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
148668
How to show $A\times (B\cup C) = (A\times B)\cup (A\times C)$
109070
Question about the proof of the distributive property for sets
95800
Prove that if $\mathcal P(A) \cup \mathcal P(B)= \mathcal P(A\cup B)$ then either $A \subseteq B$ or $B \subseteq A$.
57943
If $G$ is a convex set, prove that $\mathbb{C}\cup\{\infty\}\setminus G$ is connected.
86977
If $\cup \mathcal{F}=A$ then $A \in \mathcal{F}$. Prove that $A$ has exactly one element.
13132
If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$)
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
12472
Let $X$ and $Y$ be countable sets. Then $X\cup Y$ is countable