Forming a further commission is possible
Source: Germany 2013 - Problem 5
December 5, 2022
combinatoricsSetsIntersection
Problem Statement
Five people form several commissions to prepare a competition. Here any commission must be nonempty and any two commissions cannot contain the same members. Moreover, any two commissions have at least one common member.
There are already commissions. Prove that at least one additional commission can be formed.