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Posted by **Gaye** on Wednesday, August 31, 2011 at 3:44pm.

- Maths -
**MathMate**, Wednesday, August 31, 2011 at 7:38pmLet 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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