Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B \subseteq U$. Prove that $A \subseteq B$ iff $(U\setminus B) \subseteq (U\setminus A).$
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
140440
Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
151852
How to prove $A \subset B \iff A \cup B = B$
23764
Proving that $A+A \not\subset 2A $ using a particular definition for sum of sets
122271
A subset of a transitive set is transitive
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
119084
How many ordered pairs $(A,B)$ they are if $A$ and $B$ are subsets of $\{ 1,2,3,4,5 \}$ such that $A \cap B = \{1\}$?
49143
Showing $A \subset B \iff A\cap B=A$
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
76826
Are there sets $A$ and $B$ such that $A \in B$ and $B \in A$?
90434
Prove for every two sets $A$ and $B$ that $A-B$, ${B-A}$ and $A \cap B$ are pairwise disjoint.
93771
Prove that for any set $A$ there is some $x \notin A$
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
50939
If $A$ and $B$ are nonempty sets, prove that $A \times B = B \times A$ if and only if $A = B$
155929
Let $A, B$ be sets. Show that $\mathcal P(A ∩ B) = \mathcal P(A) ∩ \mathcal P(B)$.
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
63267
Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$