Question

设全集为R,集合A={x|-1≤x<3},B={x|2x-4≥x-2},

（1）求：A∪B,CR（A∩B);
（2）若集合C={x|2x+a＞0},满足B∪C=C，求实数a是取值范围

Answer 1

A={x|-1≤x<3}
B={x|2x-4≥x-2}
={x| x ≥ 2 }

A∪B = {x|-1≤x<3} ∪ {x| x ≥ 2 }
= { x | x≥ -1 }

CR（A∩B)
= R - (A∩B )
= R -( {x|-1≤x<3} ∩ {x| x ≥ 2 } )
=R - {x| 2 ≤x<3}
= { x | x< 2 or x ≥ 3 }

B∪C=C => B is subset of C
C={x|2x+a＞0}
= { x| x > -a/2 }

B ={x| x ≥ 2 }

=> -a/2 ≥ 2
a ≤ -4 #