prove $f(\cup A) = \cup f(A)$
48025
Image of the union is the union of the images
64586
How to prove that $\neg((A\cap B)\cup (\neg A \cap C)) = (A\cap\neg B)\cup (\neg A\cap \neg C)$
53551
$f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
94571
How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
52323
Maps - question about $f(A \cup B)=f(A) \cup f(B)$ and $ f(A \cap B)=f(A) \cap f(B)$
145397
How to prove that for every $i$, $a_i = i$
122663
Proving $T$ and $U$ are equal if I know $(X,T)$ and $(X,U)$ are hausdorff and compact
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
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
75614
Proving that $n|m\implies f_n|f_m$
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
47135
Prove if a = b, then f(a) = f(b) for any function f (with natural deduction)
68781
proving if $a \le b$ then $\sup(A) \le \inf(B)$
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
86977
If $\cup \mathcal{F}=A$ then $A \in \mathcal{F}$. Prove that $A$ has exactly one element.
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?