# My first HackMD note (change me!)

Tutaj można pobawić się markdownem - dokument jest wspólny więc bawiąc się proszę nie kasujcie poniższych przykładów.

###### Algebra relacji:

$\pi, \sigma, \rho, \times, \cup, \cap, \Join$
$\sigma_{A=102 \vee B = 'Piotrek'}(R_1)\times R_2$
x

###### Symbole do operacji logicznych w Latex-u:

$$
\vee \wedge \implies \equiv \iff \forall \exists \neg \neq \leq
$$x

#### Diagram E-R

https://graphviz.gitlab.io/_pages/pdf/dotguide.pdf

		digraph ER{
        nodesep=1.0
        label="Diagram E-R"
        edge[arrowhead=no]
        node[shape=ellipse];
    
    # sets of entities
    
        Book[shape=box];
        Customer[shape=box];
        Author[shape=box];
        
      
    # attributes of Book
        BId[label=<<u>ID</u>>]
        BTitle[label="Title \n text\n NOT NULL"]
        BId->Book
        BTitle->Book
        
    #  attributes of Customer
        Name
        Customer -> Name
        CId[label=<<u>ID</u>>]
        Customer -> CId
        AmountDue[style=dashed label="Amount due"]
        Customer -> AmountDue
        
    #  attributes of Author
        ID -> Author
        first_name -> Author
        last_name -> Author
        
    
    #  comment attached somewhere
        Comment[shape=plaintext label="aggregated\n from loans"]
        AmountDue -> Comment[style=invis]
        
    # relationships
        Loan[shape=diamond];
        LAmount[label="Amount \n Decimal(5,2)"]
        Loan->LAmount
        
    
    # edges
        Loan->Book;
        Customer->Loan[dir=back,penwidth=3.0,arrowhead=normal];

    # relationships 
        Has[shape=diamond];
    # edges
        Author->Has[dir=back, arrowhead=normal];
        Has -> Book[penwidth=3.0];
    # tak samo wysoko:
    {rank=same; Book, Customer, Loan}
}

#### Lista 2
##### Zadanie 3
$\{a\mid\ (\exists b)(R(a,b)\wedge\neg((\exists a') a'>a\ \wedge (\exists b')(R(a',b'))))\}$
$\{a,b\mid (\forall c)(T(c,a)\vee T(c,b)\vee (\forall d)(\neg T(c,d)))\}$
$\{a,b\mid S(a,b)\wedge \neg(\exists c)(T(a,c)\vee T(b,c))\}$

##### Zadanie 4
$\{o\mid (\exists b)(B(o,b))\wedge \neg(\exists b)(B(o,b)\wedge (\forall s)(P(s,b)\Rightarrow \neg L(o,s)))\}$
$\{o\mid (\exists b)(B(o,b))\wedge \neg(\exists b)(B(o,b)\wedge (\forall s)(P(s,b)\Rightarrow L(o,s)))\}$
$\{o\mid (\exists b)(B(o,b))\wedge (\forall b)(B(o,b)\Rightarrow (\exists s)(P(s,b)\wedge L(o,s)))\}$
$\{o\mid (\exists b)(B(o,b))\wedge (\forall b)(B(o,b)\wedge (\exists s)(P(s,b)\wedge L(o,s)))\}$

##### Zadanie 5
$\{o\mid (\exists b)(B(o,b)\wedge \neg(\exists b')(B(o,b')))\}$
$\{o\mid (\exists b)(B(o,b)\}$
$\{o\mid (\exists b)(B(o,b)\wedge \neg(\exists b')(b\not= b' \wedge B(o,b')))\}$
$\{o\mid (\exists b)(B(o,b)\wedge \neg(\exists b',o')(b\not= b' \wedge o=o' \wedge B(o',b')))\}$

###### 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

- [ ] 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.

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

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

:::

> 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!


- [ ] 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：

var s = "JavaScript syntax highlighting";
alert(s);



- UML diagrams

Alice->Bob: Hello Bob, how are you?
Note right of Bob: Bob thinks
Bob-->Alice: I am good thanks!
Note left of Alice: Alice responds
Alice->Bob: Where have you been?

- Auto-generated Table of Content
[ToC]

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

- Embed YouTube Videos

{%youtube PJuNmlE74BQ %}

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

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