Đáp án:
\(\eqalign{
& a)\,\, - 1 \le m \le 1 \cr
& b)\,\,1 < m < 3 \cr
& c)\,\,m \in \emptyset \cr
& d)\,\,\left[ \matrix{
m \le 1 \hfill \cr
m \ge 3 \hfill \cr} \right. \cr} \)
Giải thích các bước giải:
$$\eqalign{
& A = \left[ {m;m + 2} \right];\,\,B = \left[ {2m - 1;2m + 3} \right] \cr
& a)\,\,A \cap B = A \Leftrightarrow A \subseteq B \cr
& \Rightarrow 2m - 1 \le m < m + 2 \le 2m + 3 \cr
& \Leftrightarrow \left\{ \matrix{
m \le 1 \hfill \cr
m \ge - 1 \hfill \cr} \right. \Leftrightarrow - 1 \le m \le 1 \cr
& b)\,\,A\backslash B = A \Leftrightarrow A \cap B = \emptyset \cr
& \Rightarrow \left[ \matrix{
m + 2 < 2m + 1 \hfill \cr
2m + 3 < m \hfill \cr} \right. \Leftrightarrow \left[ \matrix{
m > 1 \hfill \cr
m < 3 \hfill \cr} \right. \Leftrightarrow 1 < m < 3 \cr
& c)\,\,A \cup B = A \cr
& \Leftrightarrow B \subseteq A \cr
& \Rightarrow m \le 2m - 1 < 2m + 3 \le m + 2 \cr
& \Leftrightarrow \left\{ \matrix{
m \ge 1 \hfill \cr
m \le - 1 \hfill \cr} \right. \Rightarrow m \in \emptyset \cr
& d)\,\,A \cap B \ne \emptyset \Leftrightarrow \left[ \matrix{
m \le 1 \hfill \cr
m \ge 3 \hfill \cr} \right. \cr} $$
