For all sets $A$ and $B$, ( $A \cap B = A \cup B \implies A = B$ )
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
49143
Showing $A \subset B \iff A\cap B=A$
67709
Stuck with proof for $\forall A\forall B(\mathcal{P}(A)\cup\mathcal{P}(B)=\mathcal{P}(A\cup B)\rightarrow A\subseteq B \vee B\subseteq A)$
134071
If A is a finite set and B is an infinite set, then B\A is an infinite set
86505
Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$
52323
Maps - question about $f(A \cup B)=f(A) \cup f(B)$ and $ f(A \cap B)=f(A) \cap f(B)$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
106564
Suppose $A,B,C$ are sets. Prove that $A\mathbin\triangle B\subseteq C \iff A\cup C=B\cup C$.
140440
Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
136835
ZF Set Theory - If $|A|^{|B|} = |B|$, then $|A| = 1 = |B|.$
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
111763
True or False $A - C = B - C $ if and only if $A \cup C = B \cup C$
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
53551
$f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
123979
Checking proof for: It is possible to find addition assumptions on the sets $A$ and $B$, so $P(A)\cup P(B) = P(A\cup B)$.
95935
Prove A = $(A \cap B) \cup (A \cap B^c)$ using the distributive and associative law.