100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
Samenvatting discrete wiskunde $4.29
Add to cart
Quickly navigate to
Preview
  2.  
  3. Hogeschool Windesheim (HW)
  4.  
  5. Discrete Wiskunde

Summary

Samenvatting discrete wiskunde

4 reviews
 15 purchases
  • Course
  • Discrete Wiskunde
  • Institution
  • Hogeschool Windesheim (HW)
  • Book
  • Discrete wiskunde in de informatica

Een uitgebreide samenvatting van o.a. Proposities, Predikaten, Waarheidstabellen, verzamelingen, deelverzamelingen, machtsverzamelingen, relaties, grafen, functies en grammatica.

Preview 4 out of 68  pages

Document information

  • No
  • H1 t/m h6
  • December 11, 2016
  • 68
  • 2016/2017
  • Summary

Subjects

  • discrete wiskunde
  • software engineer
  • advanced software development

Connected book

book image

Book Title:

Author(s):

  • Edition:
  • ISBN:
  • Edition:

Written for

  • Hogeschool Windesheim (HW)
  • HBO-ICT
  • Discrete Wiskunde
All documents for this subject (1)

4  reviews

review-writer-avatar

By: thomashhopp • 6 year ago

review-writer-avatar

By: fabianvdbor • 6 year ago

review-writer-avatar

By: roderikuenk • 6 year ago

review-writer-avatar

By: apero • 7 year ago

Seller

avatar-seller
Edd92

Reviews received

Content preview

Discrete Wiskunde
Inhoud
Introductie ........................................................................................................................................................ 6
Gebruikte Notatie (algemeen) ..................................................................................................................... 6
Vergelijkingen en ongelijkheden .............................................................................................................. 6
Bewerkingen en rekenen ......................................................................................................................... 7
Verzamelingen.......................................................................................................................................... 8
Bekende getallen en verzamelingen ........................................................................................................ 9
Gebruikte Notatie (discrete wiskunde) ........................................................................................................ 9
Getallen .......................................................................................................................................................... 10
Getallenstelsels .......................................................................................................................................... 10
Decimaal ................................................................................................................................................. 10
Binair ...................................................................................................................................................... 10
Octaal ..................................................................................................................................................... 10
Hexadecimaal ......................................................................................................................................... 11
Omrekenen tussen getallenstelsels ........................................................................................................... 12
Decimaal naar binair .............................................................................................................................. 12
Binair terugrekenen naar decimaal........................................................................................................ 12
Binair naar octaal ................................................................................................................................... 13
Binair naar hexadecimaal ....................................................................................................................... 13
Bewerkingen op getallen ........................................................................................................................... 15
Geslotenheid .......................................................................................................................................... 15
Commutativiteit ..................................................................................................................................... 15
associativiteit ......................................................................................................................................... 15
Rationale getallen (ℚ) ................................................................................................................................ 15
Afronden .................................................................................................................................................... 16
Floor ....................................................................................................................................................... 16
Ceiling ..................................................................................................................................................... 16
Div en Mod (modulo) ................................................................................................................................. 16
Div........................................................................................................................................................... 16
Mod ........................................................................................................................................................ 16
Getaltheorie ............................................................................................................................................... 17
Verschil tussen delers en echte delers ................................................................................................... 17

, Priemgetallen ......................................................................................................................................... 17
Proposities ...................................................................................................................................................... 18
Propositie ................................................................................................................................................... 18
Voorbeelden van propositie: ................................................................................................................. 18
Operatoren ................................................................................................................................................. 19
Andere operatoren................................................................................................................................. 19
Negatie ¬p .............................................................................................................................................. 19
Conjunctie (en), p ∧ q............................................................................................................................. 19
Disjunctie (of), p ∨ q ............................................................................................................................... 19
Equivalentie p ⟷ q ................................................................................................................................ 20
Implicatie p  q ..................................................................................................................................... 20
Conjunctie, disjunctie, implicatie, equivalentie samen ............................................................................. 21
Waarheidstabellen ..................................................................................................................................... 22
Aantal rijen bepalen ............................................................................................................................... 22
Tautologie / Contradictie / Contingentie: .................................................................................................. 23
Absurditeit .............................................................................................................................................. 23
Herschrijfregels .......................................................................................................................................... 24
Bit operatoren ............................................................................................................................................ 26
Bitwise & (and) ....................................................................................................................................... 26
Bitwise | (or) .......................................................................................................................................... 26
Predikaten ...................................................................................................................................................... 27
Notatie predikaat: ...................................................................................................................................... 27
Domein van variabelen .......................................................................................................................... 27
Van predicaat naar propositie (binden) ..................................................................................................... 29
Toekennen van een waarde ................................................................................................................... 29
Binding met behulp van een kwantor .................................................................................................... 29
Universele Kwantor  (geldt het voor alle) ....................................................................................... 30
Existentiële kwantor  (bestaat er in ieder geval 1 waarvoor het geldt) ......................................... 30
Gebonden en vrije variabelen ................................................................................................................ 31
Predikaat met meerdere variabelen ...................................................................................................... 31
Opdracht ................................................................................................................................................ 33
Ontkenningen ......................................................................................................................................... 33
Leren lezen van predikaat in tekst ......................................................................................................... 34
Verzamelingen................................................................................................................................................ 36
Speciale verzamelingen: ......................................................................................................................... 36
Specificatie ................................................................................................................................................. 37
Expliciete specificatie ............................................................................................................................. 37

, Impliciete specificatie............................................................................................................................. 37
Venn diagrammen .................................................................................................................................. 38
Gelijkheid.................................................................................................................................................... 38
Deelverzamelingen..................................................................................................................................... 39

deelverzameling ().............................................................................................................................. 39

Superset () .......................................................................................................................................... 39

Strikte (echte) deelverzameling ()...................................................................................................... 39
Belangrijke deelverzamelingrelatie ........................................................................................................ 40
Lege verzameling.................................................................................................................................... 40
Voorbeeld opgave: ................................................................................................................................. 40
Machtsverzameling ( 𝒫 ) ............................................................................................................................ 42
Eigenschappen machtsverzameling ....................................................................................................... 43
Voorbeeldopdracht ................................................................................................................................ 43
Operatoren ................................................................................................................................................. 44
Vereniging .............................................................................................................................................. 44
Doorsnede .............................................................................................................................................. 44
Verschil ................................................................................................................................................... 44
Complement ........................................................................................................................................... 44
Disjunct................................................................................................................................................... 44
Bags (multisets) .......................................................................................................................................... 45
Multipliciteit ........................................................................................................................................... 45
Basisverzameling (distinct) ..................................................................................................................... 45
Verzamelingsnotaties ............................................................................................................................. 45
Kardinaliteit ............................................................................................................................................ 45
Subbag .................................................................................................................................................... 45
Vereniging en doorsnede (BAGS!!) ........................................................................................................ 46
Som ......................................................................................................................................................... 46
Verschil ................................................................................................................................................... 46
Relaties ........................................................................................................................................................... 47
Notatie........................................................................................................................................................ 47
Tupel ........................................................................................................................................................... 48
Volgorde van belang: (a, b, c)  (a, c, b) ................................................................................................ 48
Tripel, paar ............................................................................................................................................. 48
Cartesisch product  .................................................................................................................................. 49
R  A² ..................................................................................................................................................... 49
Binaire relaties ........................................................................................................................................... 49

, Grafen......................................................................................................................................................... 50
Begrippen ............................................................................................................................................... 50
Cykel ....................................................................................................................................................... 50
(sterk) Samenhangend / onsamenhangend........................................................................................... 50
Eigenschappen graaf .................................................................................................................................. 51
Reflexief.................................................................................................................................................. 51
Symmetrisch ........................................................................................................................................... 52
Transitief ................................................................................................................................................ 52
Functies .......................................................................................................................................................... 53
Notatie: ...................................................................................................................................................... 53
Eigenschappen van functies; ...................................................................................................................... 53
Terminologie (Domein, codomein en beeld) ............................................................................................. 54
Domein (definitiegebied) ................................................................................................................. 54
Codomein (doelverzameling)........................................................................................................... 54
Beeld....................................................................................................................................................... 54
Eigenschappen van functies ....................................................................................................................... 55
Injectieve functie .................................................................................................................................... 55
Niet injectief ........................................................................................................................................... 55
Surjectieve functies ................................................................................................................................ 55
Bijectie .................................................................................................................................................... 55
Formele taaltheorie ....................................................................................................................................... 56
Talen ........................................................................................................................................................... 56
Syntax vs. Semantiek .............................................................................................................................. 56
Compilerstappen .................................................................................................................................... 57
Alfabet  ..................................................................................................................................................... 58
Verzameling woorden ............................................................................................................................ 58
Alfabet , Taal L  * ............................................................................................................................ 58
Operatoren ................................................................................................................................................. 59
Concatenatie .......................................................................................................................................... 59
Repetitie en vereniging .......................................................................................................................... 59
Grammatica ................................................................................................................................................ 61
Grammatica G = (H, T, P, Z) .................................................................................................................... 61
Grammatica G genereert taal L(G) ......................................................................................................... 62
Afleidingen ............................................................................................................................................. 62
Contextgevoelig / Contextvrij: ................................................................................................................... 62
Contextgevoelig: .................................................................................................................................... 62
Contextvrij: ............................................................................................................................................. 62

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller Edd92. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $4.29. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

69411 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 15 years now

Start selling
$4.29  15x  sold
  • (4)
Add to cart
Added