Let
be a set of exactly
elements. A set
of subsets of
is called an
-family over
if and only if it satisfies the following three conditions:
(i) For no two sets
in
is
;
(ii) For any three sets
in
,
(iii)
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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 $X, Y$ in $F$ is $X \subseteq Y$ ;
(ii) For any three sets $X, Y,Z$ in $F$, $X \cup Y \cup Z \neq R,$
(iii) $\bigcup_{X \in F} X = R$
Školjka