ข้อสอบคณิต O-NET - 2560

$$\begin{gathered} \mathrm{จากโจทย์} \\ B \subset C \mathrm{และ} A \cap C = \varnothing \\ \mathrm{วาดภาพได้ดังรูป} \end{gathered}$$

$$\begin{gathered} \mathrm{กำหนด} "\mathrm{สมาชิกตัวแทน}" \\ \mathrm{ในแต่ละส่วน} \mathrm{จะได้} \end{gathered}$$

$$\begin{gathered} \upsilon = \left\{1, 2, 3, 4\right\} \\ A = \left\{3\right\} \\ B = \left\{1\right\} \\ C = \left\{1, 2\right\} \end{gathered}$$

$$\begin{gathered} \mathrm{จากแต่ละตัวเลือก} \\ 1. A\cap B = B\cap C \\ \left\{3\right\}\cap \left\{1\right\} = \left\{1\right\}\cap \left\{1, 2\right\} \\ \varnothing = \left\{1\right\} \to \mathrm{ผิด} \end{gathered}$$

$$\begin{gathered} 2. \left(A\cap B\right)\cup C = \varnothing \\ \left(\left\{3\right\}\cap \left\{1\right\}\right)\cup \left\{1, 2\right\} = \varnothing \\ \varnothing \cup \left\{1, 2\right\} = \varnothing \\ \left\{1, 2\right\} = \varnothing \to \mathrm{ผิด} \end{gathered}$$

$$\begin{gathered} 3. \left(A\cup B\right)\cap C = B \\ \left(\left\{3\right\}\cup \left\{1\right\}\right)\cap \left\{1, 2\right\} = \left\{1\right\} \\ \left\{1, 3\right\}\cap \left\{1, 2\right\} = \left\{1\right\} \\ \left\{1\right\} = \left\{1\right\} \to \mathrm{ถูก} \end{gathered}$$

$$\begin{gathered} 4. A-B = C-B \\ \left\{3\right\}-\left\{1\right\} = \left\{1, 2\right\}-\left\{1\right\} \\ \left\{3\right\} = \left\{2\right\} \to \mathrm{ผิด} \end{gathered}$$

$$\begin{gathered} 5. B\cup C \not\subset A\text{'} \\ \left\{1\right\}\cup \left\{1, 2\right\} \not\subset \left\{3\right\}\text{'} \\ \left\{1, 2\right\} \not\subset \left\{1, 2, 4\right\} \to \mathrm{ผิด} \end{gathered}$$