How do I prove that if $A\setminus C = B\setminus C$ and $A\cap C = B\cap C$ then $A = B$?
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
51321
Prove that $A = B = C = D$
77859
Prove or find a counter example to the claim that for all sets A,B,C if A ∩ B = B ∩ C = A ∩ C = Ø then A∩B∩C ≠ Ø
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
13026
Prove that if AB=I_m, then rk(A)=rk(B).
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
110703
How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
1821
Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
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.
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
116215
Prove that $P(A \cap B\mid C)=P(A \mid (B \cap C))P(B\mid C)$
70311
Trying to prove (A ∩ B) − C = (A − C) ∩ (B − C)
32253
How to prove $b=c$ if $ab=ac$ (cancellation law in groups)?
70307
$(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
80892
Does $\wp(A \cap B) = \wp(A) \cap \wp(B)$ hold? How to prove it?