Đáp án:
a. \(\left[ \begin{array}{l}
X = \left\{ { - 4; - 3; - 2; - 1;2;3;4} \right\}\\
X = \left\{ { - 4; - 2; - 1;0;2;3;4} \right\}\\
X = \left\{ { - 4; - 2; - 1;1;2;3;4} \right\}\\
X = \left\{ { - 4; - 3; - 2; - 1;0;2;3;4} \right\}\\
X = \left\{ { - 4; - 3; - 2; - 1;1;2;3;4} \right\}\\
X = \left\{ { - 4; - 2; - 1;0;1;2;3;4} \right\}\\
X = \left\{ { - 4; - 3; - 2; - 1;0;1;2;3;4} \right\}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
A = \left\{ { - 4; - 2; - 1;2;3;4} \right\}\\
\left| x \right| \le 4 \to \left[ \begin{array}{l}
x \le 4\\
x \ge - 4
\end{array} \right.\\
B = \left\{ { - 4; - 3; - 2; - 1;0;1;2;3;4} \right\}\\
a.Xét:A \cap B = A = \left\{ { - 4; - 2; - 1;2;3;4} \right\}\\
Do:A \subset X \subset B\\
\to \left[ \begin{array}{l}
X = \left\{ { - 4; - 3; - 2; - 1;2;3;4} \right\}\\
X = \left\{ { - 4; - 2; - 1;0;2;3;4} \right\}\\
X = \left\{ { - 4; - 2; - 1;1;2;3;4} \right\}\\
X = \left\{ { - 4; - 3; - 2; - 1;0;2;3;4} \right\}\\
X = \left\{ { - 4; - 3; - 2; - 1;1;2;3;4} \right\}\\
X = \left\{ { - 4; - 2; - 1;0;1;2;3;4} \right\}\\
X = \left\{ { - 4; - 3; - 2; - 1;0;1;2;3;4} \right\}
\end{array} \right.
\end{array}\)
\(\begin{array}{l}
A = \left\{ { - 4; - 2; - 1;2;3;4} \right\}\\
\left| x \right| \le 4 \to \left[ \begin{array}{l}
x \le 4\\
x \ge - 4
\end{array} \right.\\
B = \left\{ { - 4; - 3; - 2; - 1;0;1;2;3;4} \right\}\\
a.Xét:A \cap B = A = \left\{ { - 4; - 2; - 1;2;3;4} \right\}\\
Do:A \subset X \subset B\\
\to \left[ \begin{array}{l}
X = \left\{ { - 4; - 3; - 2; - 1;2;3;4} \right\}\\
X = \left\{ { - 4; - 2; - 1;0;2;3;4} \right\}\\
X = \left\{ { - 4; - 2; - 1;1;2;3;4} \right\}\\
X = \left\{ { - 4; - 3; - 2; - 1;0;2;3;4} \right\}\\
X = \left\{ { - 4; - 3; - 2; - 1;1;2;3;4} \right\}\\
X = \left\{ { - 4; - 2; - 1;0;1;2;3;4} \right\}\\
X = \left\{ { - 4; - 3; - 2; - 1;0;1;2;3;4} \right\}
\end{array} \right.\\
b.Do:X = B = \left\{ { - 4; - 3; - 2; - 1;0;1;2;3;4} \right\}
\end{array}\)
Mà đề bài yêu cầu X có 4 phần tử
=> Không tồn tại tập X thỏa mãn đề bài
