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Problems
Contests
National and Regional Contests
Italy Contests
Italy TST
1996 Italy TST
2
2
Part of
1996 Italy TST
Problems
(1)
italy TST
Source: Italian IMO Team Selection Test 1996
5/5/2017
2. Let
A
1
,
A
2
,
.
.
.
,
A
n
A_1,A_2,...,A_n
A
1
,
A
2
,
...
,
A
n
be distinct subsets of an n-element set
X
X
X
(
n
≥
2
n \geq 2
n
≥
2
). Show that there exists an element
x
x
x
of
X
X
X
such that the sets
A
1
∖
{
x
}
A_1\setminus \{x\}
A
1
∖
{
x
}
,:.......,
A
n
∖
{
x
}
A_n\setminus \{x\}
A
n
∖
{
x
}
are all distinct.
combinatorics
Sets
boolean lattice method