Set Operasi: Interseksi

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:

Commutative Property: A ∩ B = B ∩ A
Associative Property: (A ∩ B) ∩ C = A ∩ (B ∩ C)
Distributive Property: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

Examples:

If A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}
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