MathDB
Intersection of elements of a family

Source: Iran TST 2008

May 25, 2008
floor functioninductioncombinatorics proposedcombinatoricsboolean lattice method

Problem Statement

Let S S be a set with n n elements, and F F be a family of subsets of S S with 2^{n\minus{}1} elements, such that for each A,B,CF A,B,C\in F, ABC A\cap B\cap C is not empty. Prove that the intersection of all of the elements of F F is not empty.