MathDB

Suppose that

\mathcal F

is a family of subsets of

X

A,B

are two subsets of

X

s.t. each element of

\mathcal{F}

has non-empty intersection with

A, B

. We know that no subset of

X

with n \minus{} 1 elements has this property. Prove that there is a representation

A,B

in the form A \equal{} \{a_1,\dots,a_n\} and B \equal{} \{b_1,\dots,b_n\}, such that for each

1\leq i\leq n

, there is an element of

\mathcal F

containing both

a_i, b_i

Problem Statement