Prove $(A\cup C=B\cup C)\implies(A\mathbin{\Delta} B\subseteq C)$
106564
Suppose $A,B,C$ are sets. Prove that $A\mathbin\triangle B\subseteq C \iff A\cup C=B\cup C$.
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.
102917
Proving statement - $(A \setminus B) \cup (A \setminus C) = B\Leftrightarrow A=B , C\cap B=\varnothing$
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
127656
How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?
29198
How to prove the following inequality $|\prod_{i=1}^{i=n}a_i-\prod_{i=1}^{i=n}b_i| < n\delta$?
5132
Given $A\cap \overline{B}\neq \emptyset$, prove $A\cup B$ connected.
87327
Unions and intersections: $(A \cup B = A ∪ C) \land (A \cap B = A ∩ C) \implies B = C.$
28641
Suppose $Y\subset X$ and $X,Y$ are connected and $A,B$ form separation for $X-Y$ then, prove that $Y\cup A$ and $Y\cup B$ are connected
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
64586
How to prove that $\neg((A\cap B)\cup (\neg A \cap C)) = (A\cap\neg B)\cup (\neg A\cap \neg C)$
123890
Show $A\setminus (A\cap B)=(A\cup B)\setminus B$
143735
Prove/Disprove: For any sets $X$ and $Y$, $\overline{X\cap Y} = \bar{X}\cup\bar{Y}$
41099
If $A \subseteq C$ and $B \subseteq D$ then $A \times B \subseteq C \times D$
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
120562
If A is an infinite set and B is at most countable set, prove that A and $A \cup B$ have the same cardinality
43462
Disprove $\mathcal{P}(A\Delta B) \setminus \{\emptyset\} = \mathcal{P}(A) \Delta\mathcal{P}(B) $. Is my proof good?