Set Operasi: Interseksi

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Questions and Answers

Apa maksud operasiIntersection dalam teori set?

  • Menghapus elemen yang sama dalam set A dan B
  • Menggabungkan semua elemen dalam set A dan B
  • Mencari elemen yang unik dalam set A dan B
  • Mencari elemen yang sama dalam set A dan B (correct)

Apakah sifat komutatif dalam operasi intersection?

  • A ∩ B = B ∩ A (correct)
  • A ∩ B < B ∩ A
  • A ∩ B ≠ B ∩ A
  • A ∩ B > B ∩ A

Jika A = {1, 2, 3} dan B = {2, 3, 4}, maka A ∩ B adalah?

  • {1, 4}
  • {1, 2, 3, 4}
  • {3, 4}
  • {2, 3} (correct)

Apakah kepentingan operasi intersection dalam aplikasi sebenar?

<p>Mencari elemen yang sama dalam dua set (C)</p> Signup and view all the answers

Apakah sifat pengagihan dalam operasi intersection?

<p>A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) (D)</p> Signup and view all the answers

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Study Notes

Operation Set: Intersection

Definition:

The intersection of two sets, denoted as A ∩ B, is the set of all elements that are common to both sets A and B.

Notation:

A ∩ B = {x | x ∈ A and x ∈ B}

Properties:

  1. Commutative Property: A ∩ B = B ∩ A
  2. Associative Property: (A ∩ B) ∩ C = A ∩ (B ∩ C)
  3. Distributive Property: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

Examples:

  1. If A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}
  2. If A = {a, b, c} and B = {c, d, e}, then A ∩ B = {c}

Importance:

The intersection operation is used to find the common elements between two sets, which is essential in various mathematical and real-world applications, such as:

  • Data analysis: finding common characteristics between two datasets
  • Set theory: studying the properties of sets and their relationships
  • Logic: identifying common truths between two statements

Operasi Set: Pertemuan

Definisi

  • Pertemuan dua set, dilambangkan sebagai A ∩ B, adalah set semua elemen yangcommon kepada kedua-dua set A dan B.

Notasi

  • A ∩ B = {x | x ∈ A dan x ∈ B}

Sifat-Sifat

Sifat Komutatif

  • A ∩ B = B ∩ A

Sifat Asosiatif

  • (A ∩ B) ∩ C = A ∩ (B ∩ C)

Sifat Distributif

  • A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

Contoh

  • Jika A = {1, 2, 3} dan B = {2, 3, 4}, maka A ∩ B = {2, 3}
  • Jika A = {a, b, c} dan B = {c, d, e}, maka A ∩ B = {c}

Kepentingan

  • operasi pertemuan digunakan untuk mencari elemen yang sama di antara dua set, yang penting dalam pelbagai aplikasi matematik dan dunia sebenar, seperti:
  • Analisis data: mencari ciri-ciri yang sama di antara dua set data
    • Teori set: kajian sifat-sifat set dan hubungan mereka
    • Logik: mengenalpasti kebenaran yang sama di antara dua pernyataan

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