Intersection of elements of a family
Source: Iran TST 2008
May 25, 2008
floor functioninductioncombinatorics proposedcombinatoricsboolean lattice method
Problem Statement
Let be a set with elements, and be a family of subsets of with 2^{n\minus{}1} elements, such that for each , is not empty. Prove that the intersection of all of the elements of is not empty.