Question

列出集合｛123456｝的64个子集

Answer 1

第一个: 空集
含1个元素的有: 6个
含2个元素的有: 1,2 1,3 1,4 1,5 1,6 2,3 2,4 2,5 2,6 3,4 3,5 3,6 4,5 4,6 5,6
15个
含3个元素的有: 1,2,3 1,2,4 1,2,5 1,2,6 1,3,4 1,3,5 1,3,6 1,4,5 1,4,6 1,5,6
2,3,4 2,3,5 2,3,6 2,4,5 2,4,6 3,4,5 3,4,6 4,5,6, 1,3,5 2,4,6 20个
含4个元素的有: (利用含2个元素的集合)3,4,5,6 2,4,5,6 2,3,5,6, 2,3,4,6 2,3,4,5 1,4,5,6 1,3,5,6 1,3,4,6 1,3,4,5 1,2,5,6 1,2,4,6 1,2,4,5 1,2,3,6 1,2,3,5 1,2,3,4 15个
含5个元素的有:2,3,4,5,6 1,3,4,5,6 1,2,4,5,6 1,2,35,6 1,2,3,4,6 1,2,3,4,5 6个
含6个元素的有:1个
以上一共64个

Answer 2

Φ,{1},{2},{3},{4},{5},{6},{1,2},{1,3},{1,4},{1,5},{1,6},{2,3},{2,4},{2,5},{2,6},{3,4},{3,5},{3,6},{4,5},{4,6},{5,6},{1,2,3},{1,2,4},{1,2,5},{1,2,6},{1,3,4},{1,3,5},{1,3,6},{1,4,5},{1,4,6},{1,5,6},{2,3,4},{2,3,5},{2,3,6},{2,4,5},{2,4,6},{2,5,6},{3,4,5},{3,4,6},{3,5,6},{4,5,6},{1,2,3,4},{1,2,3,5},{1,2,3,6},{1,2,4,5},{1,2,4,6},{1,2,5,6},{1,3,4,5},{1,3,4,6},{1,3,5,6},{1,4,5,6},{2,3,4,5},{2,3,4,6},{2,3,5,6},{2,4,5,6},{3,4,5,6},{1,2,3,4,5},{1,2,3,4,6},{1,2,3,5,6},{1,2,4,5,6},{1,3,4,5,6},{2,3,4,5,6},{1,2,3,4,5,6}