A,B,C,D,E 中有 25,9,17,20,10 个元素。A∈B∪C，B∩D∈E，求 A∩D' 中元素个数最小值

fogking

设A,B,C,D,E是全集U的子集。A,B,C,D,E的元素数分别为25,9,17,20,10。且\(A\subset B\cup C{,}\ B\cap D\subset E\)。\(A\cap\overline{D}\)的最小可能元素数是多少？

fogking

谁能回答这个问题？

fungarwai

\(A\cap\overline{D}=A-D\)
\(|A\cap\overline{D}|\ge|A|-|D|=25-20=5\)

可取：
\(A=\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25\}\)
\(B=\{1,2,3,4,5,6,7,8,9\}\)
\(C=\{9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25\}\)
\(D=\{6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25\}\)
\(E=\{1,2,3,4,5,6,7,8,9,10\}\)