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Hiệu của hai tập hợp. Phần bù

Tập hợp gồm các phần tử thuộc tập hợp A nhưng không thuộc B gọi là hiệu của A và B. Kí hiệu: (A{rm{backslash }}B)
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1. Lý thuyết

+ Định nghĩa: hiệu của A và B

Tập hợp gồm các phần tử thuộc tập hợp A nhưng không thuộc B gọi là hiệu của A và B.

+ Kí hiệu: \(A{\rm{\backslash }}B\)

Và \(A{\rm{\backslash }}B = \{ x \in A|x \notin B\} \)

+ Định nghĩa: Phần bù

Nếu \(A \subset B\) thì hiệu \(A{\rm{\backslash }}B\) gọi là phần bù của A trong B.

+ Kí hiệu: \({C_B}A\)

+ Biểu đồ Ven

 

+ Xác định hiệu của A và B

Bước 1: Biểu diễn hai tập hợp đó trên trục số.Bước 2: Gạch bỏ những phần thuộc B trong A. Khi đó phần không bị gạch là hiệu của A và B.

 

2. Ví dụ minh họa

Ví dụ 1♔. Cho tập hợp \(C = \{ 2;3;5;7\} \) và \(D = \{  - 1;3;4;5;9\} \)

Tập hợp \(C{\rm{\backslash }}D = \{ 2;7\} \)

Ví dụ 2.ඣ Cho tập hợp \(A = ( - 3;5]\) và \(B = [1; + \infty )\). Xác định \(A{\rm{\backslash }}B\) và \({C_\mathbb{R}}\left( {A \cap B} \right)\).

 Vậy \(A{\rm{\backslash }}B = ( - 3;1)\)Ta có: \(A \cap B = ( - 3;5] \cap [1; + \infty ) = [1;5]\)Suy ra \({C_\mathbb{R}}\left( {A \cap B} \right) = \mathbb{R}{\rm{\backslash }}[1;5] = ( - \infty ;1) \cup (5; + \infty )\)

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