How to prove this? "For all sets $A,B\subseteq D$ and functions $f:D\mapsto R$, we have $f(A\cap B)\subseteq(f(A)\cap f(B))$."
41477
Prove $f(S \cap T) \subseteq f(S) \cap f(T)$
6098
Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$
79697
If $A$ is a subset of $B$, then the closure of $A$ is contained in the closure of $B$.
99927
The closure of $\{ z:|f(z)|<c\}$ is the set $\{z:|f(z)|\leq c\}$.
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
119084
How many ordered pairs $(A,B)$ they are if $A$ and $B$ are subsets of $\{ 1,2,3,4,5 \}$ such that $A \cap B = \{1\}$?
111538
If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?
88201
Suppose $X$ is a finite set and $f : X \to X$ is a function. Then $f$ is injective if and only if $f$ is surjective.
138105
Let $f$ and $g$ be continuous at $ x=a$, with $f(a)<g(a)$. Prove that there exists a neighborhood $I$ of a such that $f(x)<g(x)$ for all $x \in I$.
98399
Suppose $f$ and $g$ are entire functions, and $|f(z)| \leq |g(z)|$ for all $z \in \mathbb{C}$, Prove that $f(z)=cg(z)$.
80876
Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
41099
If $A \subseteq C$ and $B \subseteq D$ then $A \times B \subseteq C \times D$
45370
Is it true that $|d(x, z) - d(y, z)| \leq d(x, y)$ and how do I prove it?
80759
Proving $A\times (B\cap C)=(A \times B)\cap (A\times C)$.
22854
Let $A , B\subseteq\mathbb{R}$. If $A$ is closed and $B$ is compact, is $A\cdot B$ closed?
103441
Proving $(A\cup B)\cap(B\cup C)\cap(C\cup A)=(A\cap B)\cup (A\cap C)\cup (B\cap C)$?