Posted by Gaye on Wednesday, August 31, 2011 at 3:44pm.
Let x = number who play both
then 3x = number who play neither.
C = set of people who play chess
T = set of people who play tennis
U = total membership of the club
By the principle of inclusion-exclusion,
|C∪T| = |C| + |T| - |C∩T|
or
|U| - |C∪T| = |U| - (|C| + |T| - |C∩T|)
3x = 47 - (18+13-x)
2x = 16
x = 8 (number of members who play both)
3x = 24 (number of members who play neither)
Total number of players
= |C∪T|
= |C| + |T| - |C∩T|
= 18 + 13 - 8
= 23
Check:
|U|=|C∪T|+24
= 23+24
=47 OK
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