Prove that f(A∩B) is a subset f(A)∩f(B)
80199
Do we have always $f(A \cap B) = f(A) \cap f(B)$?
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
134071
If A is a finite set and B is an infinite set, then B\A is an infinite set
118332
proof $f(\overline{A})\subseteq \overline{f(A)} \Leftrightarrow f$ continuous
80916
How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?
123613
Double Complement of a set proof
20335
If $A\subset B$ then $\bar{A}\subset \bar{B}$
93771
Prove that for any set $A$ there is some $x \notin A$
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
136789
How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?
9268
Proving that the Union of Two Compact Sets is Compact
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
146664
The union of two linearly independent subsets
49143
Showing $A \subset B \iff A\cap B=A$
114599
$A \cup B$ and $A \cap B$ connected $\implies A$ and $B$ are connected