题(2014年江苏预赛第9题)设集合S={1,2,…,8},A,B是S的两个非空子集,且A中的最大数小于B中的最小数,则这样的集合对(A,B)的个数是_____.解当A中最大数为1时,A有20个,B可以是集合{2,3,…,8}任意非空子集,有27-1个;当A中最大数为2时,集合{1}的子集有21个,所以A有21个,B可以是集合{3,4,…,8}的任意非空子集,有26-1个; Let’s suppose that the set S = {1,2, ..., 8}, A and B are two non-empty sub-sets of S, and the maximum number in A is smaller than the minimum number in B, then Such a collection of (A, B) the number of _____. Solutions when the maximum number of A is 1, A has 20, B can be set {2,3, ..., 8} any non-empty subset, there 27-1. When the maximum number of A is 2, there are 21 subsets of {1}, so A has 21, B can be any non-empty subset of {3,4, ..., There are 26-1