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IMO Longlists
1979 IMO Longlists
57
57
Part of
1979 IMO Longlists
Problems
(1)
Necessary and sufficient condition for the existence of a se
Source: ILL 1979 - Problem 57.
6/5/2011
Let
M
M
M
be a set and
A
,
B
,
C
A,B,C
A
,
B
,
C
given subsets of
M
M
M
. Find a necessary and sufficient condition for the existence of a set
X
⊂
M
X\subset M
X
⊂
M
for which
(
X
∪
A
)
\
(
X
∩
B
)
=
C
(X\cup A)\backslash(X\cap B)=C
(
X
∪
A
)
\
(
X
∩
B
)
=
C
. Describe all such sets.
combinatorics unsolved
combinatorics