Given $A \subset U$ and $B \subset U$. Prove or disprove $A - B \ = \emptyset \implies A \subset B$
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
5132
Given $A\cap \overline{B}\neq \emptyset$, prove $A\cup B$ connected.
28391
Prove the compactness of a set B
109070
Question about the proof of the distributive property for sets
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
43504
Proving the existence of a complement subspace $U' \subset V$.
58285
Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$
142026
Show that $A∩B∩C= ∅$ is only true when $A∩B = ∅, A∩C = ∅$ or $B∩C = ∅$ or show a counterexample.
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
89712
For every set $A$, the empty set is a subset of $A$. The empty set is a set. Therefore, the empty set has a cardinality $\geq 1\ldots$
106564
Suppose $A,B,C$ are sets. Prove that $A\mathbin\triangle B\subseteq C \iff A\cup C=B\cup C$.
70307
$(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
132971
Prove that $|a| < b \iff -b<a<b$
123613
Double Complement of a set proof
1821
Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
50939
If $A$ and $B$ are nonempty sets, prove that $A \times B = B \times A$ if and only if $A = B$
43068
Let A and B be sets. Show that A is a subset of B if and only if for any set C, one has A union C is a subset of B union C.