Proof of $f(A∩B)⊆f(A)∩f(B)$
41477
Prove $f(S \cap T) \subseteq f(S) \cap f(T)$
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
49592
Show that, if $f:A\to B$ is a function, with $A$ and $B$ being finite sets, and $|A|=|B|$, then $f$ is one to one iff $f$ is onto.
123613
Double Complement of a set proof
64320
Prove that if $0<a<Pr(A)$ then there exists $B\subset A$ such that $Pr(B)=a$
90619
For closed subsets $A,B \subseteq X$ with $X = A \cup B$ show that $f \colon X \to Y$ is continuous iff $f|_A$ and $f|_B$ are continuous.
155063
Is Cl(f(A)) a subset of f(Cl(A))?
86317
Show that $F\subset Y$ is closed in $Y$ iff $F=Y\;\cap\;H$ where $H\subset X$ is closed in $X$.
90434
Prove for every two sets $A$ and $B$ that $A-B$, ${B-A}$ and $A \cap B$ are pairwise disjoint.
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
49143
Showing $A \subset B \iff A\cap B=A$
70552
Prove that $\mathcal{P}(A)⊆ \mathcal{P}(B)$ if and only if $A⊆B$.
9268
Proving that the Union of Two Compact Sets is Compact
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
80876
Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
13253
Prove $f(S \cup T) = f(S) \cup f(T)$