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CIIM
2014 CIIM
Problem 3
Problem 3
Part of
2014 CIIM
Problems
(1)
CIIM 2014 Problem 3
Source:
8/9/2016
Given
n
≥
2
n\geq2
n
≥
2
, let
A
\mathcal{A}
A
be a family of subsets of the set
{
1
,
2
,
…
,
n
}
\{1,2,\dots,n\}
{
1
,
2
,
…
,
n
}
such that, for any
A
1
,
A
2
,
A
3
,
A
4
∈
A
A_1,A_2,A_3,A_4 \in \mathcal{A}
A
1
,
A
2
,
A
3
,
A
4
∈
A
, it holds that
∣
A
1
∪
A
2
∪
A
3
∪
A
4
∣
≤
n
−
2
|A_1 \cup A_2 \cup A_3 \cup A_4| \leq n -2
∣
A
1
∪
A
2
∪
A
3
∪
A
4
∣
≤
n
−
2
. Prove that
∣
A
∣
≤
2
n
−
2
.
|\mathcal{A}| \leq 2^{n-2}.
∣
A
∣
≤
2
n
−
2
.
CIIM
CIIM 2014
undergraduate