Question

A={x|1-x分之3属于Z},则集合A的非空真子集的个数是几个,并一一列举

Answer 1

3/(1-x)∈Z,

所以 1-x=1,3,-1,-3

解得 x=0,-2,2,4

从而 A={0,-2,2,4}

它的非空真子集有2⁴-2=14个.

分别是{0}、{－2}、{2}、{4}、{0,－2}、{0,2}、{0,4}、{－2,2}、{－2,4}、{2,4}

{0,－2,2}、{0,－2,4}、{0,2,4}、{－2,2,4}.