MathDB

Let

S

be a set consisting of

n

elements,

F

a set of subsets of

S

consisting of

2^{n-1}

subsets such that every three such subsets have a non-empty intersection. a) Show that the intersection of all subsets of

F

is not empty. b) If you replace the number of sets from

2^{n-1}

with

2^{n-1}-1

, will the previous answer change?

3