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Solving Lesson 54 Page 17 Math 10 SBT – Kite>

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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 \(B\backslash A = \emptyset \)

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