Question

高中集合问题

高中集合问题题目如图，只要挑战2

Answer 1

A={x|-1≤x≤2}

B={x| x^2-(2m+1)x+2m<0 } ={ x| (x-2m)(x-1)<0 }

case 1: m< 1/2

B={ x| (x-2m)(x-1)<0 } = { x| 2m<x<1 }

AUB =A

=> B 是A的子集

2m≥-1

m≥-1/2

solution for case 1: -1/2≤m <1/2

case 2: m=1/2

B={ x| (x-2m)(x-1)<0 } = { x|  (x-1)^2 < 0 }  =Φ

B 是A的子集

solution for case 2: m=1/2

case 3: m>1/2

B={ x| (x-2m)(x-1)<0 } = { x| 1<x<2m }

A={x|-1≤x≤2}

B 是A的子集

2m≤2  

m≤1/2

case 3: 舍去

ie

AUB =A

=> case 1 or case 2 or case 3

=>-1/2≤m <1/2or  m=1/2

=> -1/2≤m≤ 1/2