---
# System prepended metadata

title: Untitled

---

先看這個基本排版可以左右對照

https://hackmd.io/features-tw?both

常見latex符號
https://en.wikipedia.org/wiki/Wikipedia:LaTeX_symbols
https://en.wikibooks.org/wiki/LaTeX/Mathematics

1. Given $A=\left\{1,2,3\right\}$, is $\emptyset\subset A$?
   - Yes.
   - If $E\subset F$ then every element of $E$ is in $F$. 
     Since no element is in $\emptyset$, $\emptyset\subset A$ is trivially true.
   - If $E\subset F$ then $E\in 2^F$, where $2^F=\left\{\emptyset,\left\{1\right\},\left\{2\right\},\left\{3\right\},\left\{1,2\right\},\left\{2,3\right\},\left\{1,3\right\},A\right\}$ is the power set of $A$.
2. $\emptyset\in A$ when $A\neq\emptyset$.
   - Yes.
   - For example, if $A=\left\{1,2,3\right\}$ then $\emptyset\notin A$. But if $A=\left\{\emptyset,1,2,3\right\}$ then $\emptyset\in A$.

3. $A\subseteq\emptyset$ when $A\neq\emptyset$.
   - No.
   - By 1. The power set of $\emptyset$ is $\left\{\emptyset\right\}$. So $A\subseteq\emptyset$ only if $A=\emptyset$.

4. $\left\{\emptyset\right\}\subset A$ when $A\neq\emptyset$.
   - Yes. 
   - For example, if $\left\{\left\{\emptyset\right\},1,2,3\right\}$
        
   
5. $A\subset\emptyset$.
   - No. 
   - Always false. The power set of $\emptyset$ is $\left\{\emptyset\right\}$. But $A\neq\emptyset$.

NOTE:
   - $\emptyset\subset A$ when $A\neq\emptyset$

4. original answer
   - No. The power set of $A$ contains $\emptyset$ so $\emptyset\subset A$ as in 1. But not $\left\{\emptyset\right\}\subset A$.
   - No. $\emptyset\in\left\{\emptyset\right\}$ but $\emptyset$ may not be in $A$ as in 2.

$$\left( 括號裏面的字 \right)$$
$$\left[ 括號裏面的字 \right]$$
$$\left< 括號裏面的字 \right>$$
$$\left\{ 括號裏面的字 \right\}$$
注意{跟}前面的\ , 因爲{跟}是保留符號, 所以要加\

分數:
$$\frac{分子}{分母}$$