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Samenvatting Wiskunde D VWO Combinatoriek $4.30   Add to cart

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Samenvatting Wiskunde D VWO Combinatoriek

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Samenvatting Getal & Ruimte Wiskunde D vwo H1 Combinatoriek

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  • Hoofdstuk 1
  • March 28, 2021
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  • 2020/2021
  • Summary
  • Secondary school
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Wiskunde D- H1 Combinatoriek
Verzamelingen
Begrippen:
- 𝑁𝑎𝑡𝑢𝑢𝑟𝑙𝑖𝑗𝑘𝑒 𝑔𝑒𝑡𝑎𝑙𝑙𝑒𝑛; ℕ = {0, 1, 2, 3, 4, … }
- 𝐺𝑒ℎ𝑒𝑙𝑒 𝑔𝑒𝑡𝑎𝑙𝑙𝑒𝑛; ℤ = {… , −3, −2, −1, 0, 1, 2, 3, … }
1 1
- 𝑅𝑎𝑡𝑖𝑜𝑛𝑒𝑙𝑒 𝑔𝑒𝑡𝑎𝑙𝑙𝑒𝑛; ℚ = {… , −1, − 2 , 0, 2 , 1, … }
- 𝑅𝑒ë𝑙𝑒 𝑔𝑒𝑡𝑎𝑙𝑙𝑒𝑛; ℝ = {ℕ, ℤ, ℚ, 𝜋}
- ∈ = 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑣𝑎𝑛
- ∋ = 𝑏𝑒𝑣𝑎𝑡 𝑎𝑙𝑠 𝑒𝑙𝑒𝑚𝑒𝑛𝑡
- ∨ = 𝑜𝑓
- ∧ = 𝑒𝑛
Er zijn 4 manieren om verzamelingen te noteren
1. Elementen opsommen tussen accolades: {2, 4, 6, 8}
2. Met stippen een opsomming suggereren: {2, 4, 6, 8, …}
3. Een voorwaarde vermelden waar de elementen van de verzameling aan moeten voldoen:
𝑥
{𝑥 ∈ ℕ | ∈ ℕ}
2
- Verzameling van alle natuurlijke getallen 𝑥 waarvoor geldt dat 𝑥 gedeeld door 2
een natuurlijk getal is
4. Door middel van een interval:
- 〈𝑎, 𝑏〉 = {𝑥 ∈ ℝ | 𝑎 < 𝑥 < 𝑏}
- [𝑎, 𝑏⟩ = {𝑥 ∈ ℝ | 𝑎 ≤ 𝑥 < 𝑏}
- ⟨𝑎, 𝑏] = {𝑥 ∈ ℝ | 𝑎 < 𝑥 ≤ 𝑏}

Verzamelingen kunnen in beeld worden gebracht in een venndiagram:



De doorsnede 𝑉 ∩ 𝑊 van verzameling V en W bestaat uit gemeenschappelijke
elementen van V en W:
- 𝑉 ∩ 𝑊 = {𝑥 | 𝑥 ∈ 𝑉 ∧ 𝑥 ∈ 𝑊}
- De verzamelingen V en W heten disjunct als 𝑉 ∩ 𝑊 = ∅ (lege
verzameling)




De vereniging 𝑉 ∪ 𝑊 van de verzameling V en W bestaat uit de
elementen die tot V, tot W, of tot beide behoren:
- 𝑉 ∪ 𝑊 = {𝑥 | 𝑥 ∈ 𝑉 ∨ 𝑥 ∈ 𝑊}



Het verschil 𝑉 ∖ 𝑊 van de verzamelingen V en W bestaat uit de
elementen die wel tot V, maar niet tot W behoren:
- 𝑉 ∖ 𝑊 = {𝑥 | 𝑥 ∈ 𝑉 ∧ 𝑥 ∉ 𝑊}

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