Question

已知集合A={x|2kπ-π/4<x<2kπ+π/4,k∈Z},B={Y|0<y<4π},求A∩B

Answer 1

A= {x| 0π-π/4 <x < 0π + π/4} ∪ {x| 2π-π/4 <x < 2π + π/4} ∪ {x| 4π-π/4 <x < 4π + π/4} ∪ ……

因为 当k>=3时 2kπ- π/4>4π 当k<0时 2kπ+π/4<0

所以
A∩B ={x| 0π-π/4 <x < 0π + π/4} ∪ {x| 2π-π/4 <x < 2π + π/4} ∪ {x| 4π-π/4 <x < 4π + π/4} ∩B
={x| 0< x< π/4 或 7π/4 <x <9π/4 或 15π/4<x<4π }

Answer 2

借用数轴
A∩B={x|0<x<π/4，或2π-π/4<x<2π+π/4，或4π-π/4<x<4π},
= {x|0<x<π/4，或7π/4<x<9π/4，或15π/4<x<4π}