Topic
Given two sets \(A = \left[ { – 1;4} \right],B = \left[ {m + 1;m + 3} \right]\) with m as the parameter. Find all values of m so that \(B\backslash A = \emptyset \)
Solution method – See details
Use knowledge: \(A\backslash B = \emptyset \Leftrightarrow A \subset B\) or \(A = B\)
Detailed explanation
We have: \(B\backslash A = \emptyset \Leftrightarrow B \subset A\)
To \(B \subset A\) then: \(\left\{ {\begin{array}{*{20}{c}}{m + 1 \ge – 1}\\{m + 3 \le 4 }\end{array}} \right.\) \( \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{m \ge – 2}\\{m \le 1} \end{array}} \right \Leftrightarrow – 2 \le m \le 1\)
So \( – 2 \le m \le 1\) then \(B\backslash A = \emptyset \)
