Suppose http://quicklatex.com/cache3/ql_0c45...90d6fe9_l3.png is a collection of subsets of http://quicklatex.com/cache3/ql_46ee...64355ff_l3.png that is an antichain with regards to inclusion.

Show that

http://quicklatex.com/cache3/ql_5064...5d198e5_l3.png

There is a very nice probabilistic proof of this. Note also that it is easy to deduce from this that

http://quicklatex.com/cache3/ql_f5b0...c19d361_l3.png

Moderator approved: MF