Prove that $A=B$ considering: $(A \cap C = B \cap C) \land (A \cup C = B \cup C)$
87327
Unions and intersections: $(A \cup B = A ∪ C) \land (A \cap B = A ∩ C) \implies B = C.$
70311
Trying to prove (A ∩ B) − C = (A − C) ∩ (B − C)
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
102917
Proving statement - $(A \setminus B) \cup (A \setminus C) = B\Leftrightarrow A=B , C\cap B=\varnothing$
14162
How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
140446
Prove that $A \smallsetminus (A \smallsetminus B) = A \cap B$
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
57979
If $P(A \cup B \cup C) = 1$, $P(B) = 2P(A) $, $P(C) = 3P(A) $, $P(A \cap B) = P(A \cap C) = P(B \cap C) $, then $P(A) \le \frac14$
118239
If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$
68258
Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
7416
Let $ A $, $ B $ and $ C $ be sets. If $ A \cup B = A \cup C $ and $ A \cap B = A \cap C $, then show that $ B = C $.
150738
Proof of $(A - B) - C = A - (B \cup C)$