Prove that for all $U\subseteq A$ and $V\subseteq A$, that $f(U\cup V)=f(U)\cup f(V)$.
13253
Prove $f(S \cup T) = f(S) \cup f(T)$
116527
Validating a proof for necessary and sufficient conditions on sets A & B such that $P(A) \cup P(B) = P(A\cup B)$
107383
Derived sets - prove $(A \cup B)' = A' \cup B'$
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
92376
Let $f:A \rightarrow B$ and C ⊂A. Define f[C]={b∈B: b=f(a) for some a∈C}. Prove or disprove each of the statement
80827
Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
28641
Suppose $Y\subset X$ and $X,Y$ are connected and $A,B$ form separation for $X-Y$ then, prove that $Y\cup A$ and $Y\cup B$ are connected
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
32525
If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.
59813
Prove that for all sets A and B, A ∩ B = ∅ implies ( A ∪ B ) - B = A
40604
Is this proof correct for : Does $F(A)\cap F(B)\subseteq F(A\cap B) $ for all functions $F$?
50159
How to prove if $\Bbb R^n=W_1\cup W_2\cup \cdots\cup $ where each $W_k$ is a subspace, then $\Bbb R^n=W_i$ holds for some $i$
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
75614
Proving that $n|m\implies f_n|f_m$
145058
Prove $ (A \cup B) \cap C$ = $(A \cap C) \cup (B \cap C) $
9854
If $U$ is a neighborhood of $e$, there exists $V$ neighborhood of $e$ such that $V^{-1}V \subseteq U$