Đáp án đúng: C
Cách giải nhanh bài tập nàya) Ta có : \(\left\{ \begin{array}{l}A = \left\{ {0;\,\,1;\,\,2;\,\,3} \right\}\\B = \left\{ {0;\,\,1;\,\,2;\,\,3;\,\,4} \right\}\\C = \left\{ { - 2;\,\,0;\,\,2;\,\,4} \right\}\end{array} \right..\)
b) Xác định các tập hợp sau và so sánh:
i/ Ta có : \(\left\{ \begin{array}{l}A \cup B = \left\{ {0;\,\,1;\,\,2;\,\,3;\,\,4} \right\} \Rightarrow \left( {A \cup B} \right) \cup C = \left\{ { - 2;\,\,0;\,\,1;\,\,2;\,\,3;\,\,4} \right\}\\B \cup C = \left\{ { - 2;\,\,0;\,\,1;\,\,2;\,\,3;\,\,4} \right\} \Rightarrow A \cup \left( {B \cup C} \right) = \left\{ { - 2;\,\,0;\,\,1;\,\,2;\,\,3;\,\,4} \right\}\end{array} \right..\)
Ta thấy \(\left( {A \cup B} \right) \cup C = A \cup \left( {B \cup C} \right).\)
ii/ Ta có : \(\left\{ \begin{array}{l}A \cap B = \left\{ {0;\,\,1;\,\,2;\,\,3} \right\} \Rightarrow \left( {A \cap B} \right) \cap C = \left\{ {0;\,\,2} \right\}\\B \cap C = \left\{ {0;\,\,2;\,\,4} \right\} \Rightarrow A \cap \left( {B \cap C} \right) = \left\{ {0;\,\,2} \right\}\end{array} \right..\)
Ta thấy \(\left( {A \cap B} \right) \cap C = A \cap \left( {B \cap C} \right).\)
iii/ Ta có : \(\left\{ \begin{array}{l}B \cap C = \left\{ {0;\,\,2;\,\,4} \right\} \Rightarrow A \cup \left( {B \cap C} \right) = \left\{ {0;\,\,1;\,\,2;\,\,3;\,\,4} \right\}\\A \cup C = \left\{ { - 2;\,\,0;\,\,1;\,\,2;\,\,3;\,\,4} \right\} \Rightarrow \left( {A \cup B} \right) \cap \left( {A \cup C} \right) = \left\{ {0;\,\,1;\,\,2;\,\,3;\,\,4} \right\}.\end{array} \right.\)
Ta thấy \(A \cup \left( {B \cap C} \right) = \left( {A \cup B} \right) \cap \left( {A \cup C} \right).\)
iv/ Ta có : \(\left\{ \begin{array}{l}A \cap \left( {B \cup C} \right) = \left\{ {0;\,\,1;\,\,2;\,\,3} \right\}\\A \cap C = \left\{ {0;\,\,2} \right\} \Rightarrow \left( {A \cap B} \right) \cup \left( {A \cap C} \right) = \left\{ {0;\,\,1;\,\,2;\,\,3} \right\}\end{array} \right..\)
Ta thấy : \(A \cap \left( {B \cup C} \right) = \left( {A \cap B} \right) \cup \left( {A \cap C} \right).\)