P(A) $\subset$ P(B) implies A $\subset $ B proof or disproof.
70552
Prove that $\mathcal{P}(A)⊆ \mathcal{P}(B)$ if and only if $A⊆B$.
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
109778
Proving $(x-c)|(p(x)-p(c))$
66948
Proving question on sets
142026
Show that $A∩B∩C= ∅$ is only true when $A∩B = ∅, A∩C = ∅$ or $B∩C = ∅$ or show a counterexample.
28391
Prove the compactness of a set B
10909
$|A \cup B| = \mathfrak{c}$, then $A$ or $B$ has cardinality $\mathfrak{c}$.
13132
If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$)
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
43462
Disprove $\mathcal{P}(A\Delta B) \setminus \{\emptyset\} = \mathcal{P}(A) \Delta\mathcal{P}(B) $. Is my proof good?
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
2978
A and B disjoint, A compact, and B closed implies there is positive distance between both sets
41099
If $A \subseteq C$ and $B \subseteq D$ then $A \times B \subseteq C \times D$
17212
The preimage of a subset
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
52322
Implication in mathematics - How can A imply B when A is False?