## Solving Lesson 54 Page 17 Math 10 SBT – Kite>

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 $$B\backslash A = \emptyset$$