---
# System prepended metadata

title: Participation active - groupe 1
tags: [Tag(change me!)]

---

# Participation active - groupe 1 

[toc]
> [name=flandes] toc: tabel of contents

# Bases du Markdown (et du LaTeX, surtout)

Exercice 3.3. : questions 1 a 11 

$$ \exists x \in \mathbb{R} , ( x+1 = 0 ) \wedge (x+2 = 0)$$


$$ \left( \exists x \in \mathbb{R}, x+1 = 0 \right) \wedge \left( \exists x \in \mathbb{R}, x+2 = 0 \right)$$

$$\exists z \in \mathbb{R}, \forall x \in \mathbb{R}, \forall y \in \mathbb{R}, (xy=z \implies ((x=z) \vee (y=$$ 

$$\forall z \in \mathbb{R}, \exists x \in \mathbb{R}, \forall y \in \mathbb{R}, (xy=z \implies ((x=z) \vee ($y=$$ \forall x \in \{0,1,2\}, \exists A \in \mathcal{P}(\{0,1,2\}), x \notin A$$

$$ \exists A \in \mathcal{P}(\{0,1,2\}), \forall x \in \{0,1,2\}, x \notin A$$

$$\forall A \in \mathcal{P}(\{0,1,2\}), \exists B \in \mathcal{P}(\{0,1,2\}), (A \cap B = \emptyset) \wedge (A$$ = \{0,1,2\})$$

$$\exists A \in \mathcal{P}(\{0,1,2\}), \forall B \in \mathcal{P}(\{0,1,2\}), (A \cap B = \emptyset) \wedge (A$$ = \{0,1,2\})$$

$$ \forall x \in \mathbb{R}, \exists y \in \mathbb{R}, x = y^2$$
Faux, exemple: x=-1


$$ \forall x \in \mathbb{N}, \exists y \in \mathbb{N}, x = y^2$$


$$ \forall x \in \mathbb{N}, \exists y \in \mathbb{R}, x = y^2$$


$$ x \to \infty $$

-------- 

Exercice 3.1
-> désormais inclus dans les corrigés tapés en pdf

Exercecie 2.4

A l ensembe des personnes qui parlent Allemand
B ... Bulgare
C ... chinois
$$| A \cup B \cup C| = 90$$
$$|A|=40$$
$$|B|=30$$
$$|C|=30$$
$$|A \cap B | + | B \cap C| + |A \cap C| = 30 $$

$$ | A \cap B \cap C|  =  | A \cup B \cup C|  - |A|-|B| - |C| +  |A \cap B | + | B \cap C| + |A \cap C| \\
= 90 - 40 - 30 -30 + 30 \\
=20 $$


il existe e appartient à E, T(e) implique notB(e)

$$ \exists e \in E , T(e) \implies \neg B(e)$$

$$ \exists e \in E , \neg T(e) \vee \neg B(e)$$


---- 


$\LaTeX$, c'est génial, ça permet d'écrire des maths, de façon élégante:
$$A = \overline{B \cap D} $$

$$ B= D \text{  on peut mettre des bouts de texte comme ça} $$

$$ allez y écrivez des maths ici ! - oups, des maths, pas du texte !$$

$$ f: E \rightarrow F  $$ 

$$ a \wedge \neg a \equiv \bot $$  

$$ a \vee \neg a \equiv \top $$  


-----

# My first HackMD note (change me!)

###### tags: `Tag(change me!)`

> This note is yours, feel free to play around.  :video_game: 
> Type on the left :arrow_left: and see the rendered result on the right. :arrow_right: 

## :memo: Where do I start?

### Step 1: Change the title and add a tag

- [x] Create my first HackMD note (this one!)
- [ ] Change its title
- [ ] Add a tag

:rocket: 

### Step 2: Write something in Markdown

Let's try it out!
Apply different styling to this paragraph:
**HackMD gets everyone on the same page with Markdown.** ==Real-time collaborate on any documentation in markdown.== Capture fleeting ideas and formalize tribal knowledge.

- [x] **Bold**
- [ ] *Italic*
- [ ] Super^script^
- [ ] Sub~script~
- [ ] ~~Crossed~~
- [x] ==Highlight==

:::info
:bulb: **Hint:** You can also apply styling from the toolbar at the top :arrow_upper_left: of the editing area.

![](https://i.imgur.com/Cnle9f9.png)
:::

> Drag-n-drop image from your file system to the editor to paste it!

### Step 3: Invite your team to collaborate!

Click on the <i class="fa fa-share-alt"></i> **Sharing** menu :arrow_upper_right: and invite your team to collaborate on this note!

![permalink setting demo](https://i.imgur.com/PjUhQBB.gif)

- [ ] Register and sign-in to HackMD (to use advanced features :tada: ) 
- [ ] Set Permalink for this note
- [ ] Copy and share the link with your team

:::info
:pushpin: Want to learn more? ➜ [HackMD Tutorials](https://hackmd.io/c/tutorials) 
:::

---

## BONUS: More cool ways to HackMD!

- Table

| Features          | Tutorials               |
| ----------------- |:----------------------- |
| GitHub Sync       | [:link:][GitHub-Sync]   |
| Browser Extension | [:link:][HackMD-it]     |
| Book Mode         | [:link:][Book-mode]     |
| Slide Mode        | [:link:][Slide-mode]    | 
| Share & Publish   | [:link:][Share-Publish] |

[GitHub-Sync]: https://hackmd.io/c/tutorials/%2Fs%2Flink-with-github
[HackMD-it]: https://hackmd.io/c/tutorials/%2Fs%2Fhackmd-it
[Book-mode]: https://hackmd.io/c/tutorials/%2Fs%2Fhow-to-create-book
[Slide-mode]: https://hackmd.io/c/tutorials/%2Fs%2Fhow-to-create-slide-deck
[Share-Publish]: https://hackmd.io/c/tutorials/%2Fs%2Fhow-to-publish-note

- LaTeX for formulas

$$
x = {-b \pm \sqrt{b^2-4ac} \over 2a}
$$

- Code block with color and line numbers：
```javascript=16
var s = "JavaScript syntax highlighting";
alert(s);
```

- Auto-generated Table of Content
[ToC]

> Leave in-line comments! [color=#3b75c6]

> Put your cursor right behind an empty bracket {} :arrow_left: and see all your choices.

- And MORE ➜ [HackMD Tutorials](https://hackmd.io/c/tutorials)
