How do I prove the following: $f(S\cup T) = f(S) \cup f(T)$
13253
Prove $f(S \cup T) = f(S) \cup f(T)$
10107
Prove $A\cup (A\cap B) = A$
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
47135
Prove if a = b, then f(a) = f(b) for any function f (with natural deduction)
140440
Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
151295
Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
86977
If $\cup \mathcal{F}=A$ then $A \in \mathcal{F}$. Prove that $A$ has exactly one element.
153406
$[F(t):F(t^n)]=n$ where $t$ is trascendental
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
76694
Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$
102917
Proving statement - $(A \setminus B) \cup (A \setminus C) = B\Leftrightarrow A=B , C\cap B=\varnothing$
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 $i$
123890
Show $A\setminus (A\cap B)=(A\cup B)\setminus B$
133682
Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
1821
Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality