Given sets $A,B$, there exists injection $f:A\to B$ or injection $g:B\to A$
83996
For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$
88281
Mixing and Distributing Qualifiers ($\forall x$, $\exists x$)
133699
Proving that there is a bijection between $A$ and $B$.
49143
Showing $A \subset B \iff A\cap B=A$
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
28391
Prove the compactness of a set B
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
13415
How to show if $A \subseteq B$, then $A \cap B = A$?
9149
Any $B \subset \{10,11,...,99\}$, with $|B| =10$ has two subsets such that $\sum_{a \in B_1} a = \sum_{b \in B_2} b$
83714
$A \in B$ vs. $A \subset B$ for proofs
125043
Show that F(A−B) is not necessarily a subset of F(A)−F(B).
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
155063
Is Cl(f(A)) a subset of f(Cl(A))?
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
158882
Prove the existence of some weird family of 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