If $A\cup B=A\cup C$ and $A\cap B= A\cap C$, prove that: $B=C$
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 $.
158355
If $A$ commutes with $B$ and $B$ commutes with $C$, then $A$ commutes with $C$
51321
Prove that $A = B = C = D$
30770
Prove that $C\left(\bigcup_{\alpha\in I} A_\alpha\right)=\bigcap_{\alpha\in I}C\left(A_\alpha\right)$
111763
True or False $A - C = B - C $ if and only if $A \cup C = B \cup C$
70311
Trying to prove (A ∩ B) − C = (A − C) ∩ (B − C)
95800
Prove that if $\mathcal P(A) \cup \mathcal P(B)= \mathcal P(A\cup B)$ then either $A \subseteq B$ or $B \subseteq A$.
148668
How to show $A\times (B\cup C) = (A\times B)\cup (A\times C)$
26302
Prove that $(X \cap Y) \cup Z = (X \cup Z) \cap (Y \cup Z)$
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
52323
Maps - question about $f(A \cup B)=f(A) \cup f(B)$ and $ f(A \cap B)=f(A) \cap f(B)$
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
149553
Is it always true that $(A_1 \cup A_2) \times (B_1 \cup B_2)=(A_1\times B_1) \cup (A_2 \times B_2)$
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
50266
In the following figure prove that: $AK||BC$
80892
Does $\wp(A \cap B) = \wp(A) \cap \wp(B)$ hold? How to prove it?