MathDB

Let

R

be a set of exactly

6

elements. A set

F

of subsets of

R

is called an

S

-family over

R

if and only if it satisfies the following three conditions: (i) For no two sets

X, Y

F

X \subseteq Y

;
(ii) For any three sets

X, Y,Z

F

X \cup Y \cup Z \neq R,

(iii)

\bigcup_{X \in F} X = R

Problem Statement