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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
1997 All-Russian Olympiad Regional Round
11.5
11.5
Part of
1997 All-Russian Olympiad Regional Round
Problems
(1)
factions from State Duma - All-Russian MO 1997 Regional (R4) 11.5
Source:
9/24/2024
Members of the State Duma formed factions in such a way that for any two fractions
A
A
A
and
B
B
B
(not necessarily different),
A
∪
B
‾
\overline{A \cup B}
A
∪
B
is also faction (
C
‾
\overline{C}
C
denotes the set of all members of the Duma, not including in
C
C
C
). Prove that for any two factions
A
A
A
and
B
B
B
,
A
∪
B
A \cup B
A
∪
B
is also a faction.
combinatorics