Let
be
element sets such that each two of them have a nonempty intersection. Let
be the union of all the sets
and let
be a subset of
such that for each
the intersection of
and
consists of exactly two different elements
and
. Find all subsets
of the set
with
elements satisfying the condition that for at least one index
both elements
and
belong to
.
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$(MON 3)$ Let $A_k (1 \le k \le h)$ be $n-$element sets such that each two of them have a nonempty intersection. Let $A$ be the union of all the sets $A_k,$ and let $B$ be a subset of $A$ such that for each $k (1\le k \le h)$ the intersection of $A_k$ and $B$ consists of exactly two different elements $a_k$ and $b_k$. Find all subsets $X$ of the set $A$ with $r$ elements satisfying the condition that for at least one index $k,$ both elements $a_k$ and $b_k$ belong to $X$.
Školjka