Prove that for all sets $A$ and $B$, $( A \cup B ) - B = A$ implies $A \cap B =\varnothing$.
59813
Prove that for all sets A and B, A ∩ B = ∅ implies ( A ∪ B ) - B = A
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
140446
Prove that $A \smallsetminus (A \smallsetminus B) = A \cap B$
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
87327
Unions and intersections: $(A \cup B = A ∪ C) \land (A \cap B = A ∩ C) \implies B = C.$
77286
Proving set theory question
66948
Proving question on sets
155929
Let $A, B$ be sets. Show that $\mathcal P(A ∩ B) = \mathcal P(A) ∩ \mathcal P(B)$.
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
123979
Checking proof for: It is possible to find addition assumptions on the sets $A$ and $B$, so $P(A)\cup P(B) = P(A\cup B)$.
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
138199
Proof explanation $A\setminus B = A \setminus B \cap A$
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
70307
$(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
52323
Maps - question about $f(A \cup B)=f(A) \cup f(B)$ and $ f(A \cap B)=f(A) \cap f(B)$
63267
Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$