Question

Cho \(A=(-4;5];B=\left(2m-1;m+3\right)\), tìm m sao cho:

a, \(A\subset B\)

b, \(B\subset A\)

c, \(A\cap B=\varnothing\)

d, \(A\cup B\) là một khoảng

Answer 1

a, \(A\subset B\Leftrightarrow\left\{{}\begin{matrix}m+3\ge5\\2m-1< -4\end{matrix}\right.\Rightarrow m\in\left\{\varnothing\right\}\)

b, \(B\subset A\Leftrightarrow\left\{{}\begin{matrix}m+3\le5\\2m-1>-4\end{matrix}\right.\Leftrightarrow-\dfrac{3}{2}< m\le2\)

c, \(A\cap B=\varnothing\Leftrightarrow\left[{}\begin{matrix}2m-1>5\\m+3\le-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}m>3\\m\le-7\end{matrix}\right.\)

d, \(A\cup B\) là một khoảng \(\Leftrightarrow\left\{{}\begin{matrix}m+3>5\\2m-1\le5\end{matrix}\right.\Leftrightarrow2< m\le3\)