In a class of 42 students, each play at least one of the three games-cricket,hockey or football.It is found that 14 play cricket, 20 play hockey and 24 play football. 3 play both cricket and football, 2 play both hockey and football and none play all the three games. Find the number of students who play cricket but not hockey.

Asked by Koushtav Chakrabarty | 2nd Aug, 2012, 10:03: PM

Expert Answer:

Let the set of students who play cricket, hockey and football be C, H, F respectively.
Then,
n(C) = 14, n(H) = 20, n(F) = 24, n(C intersection F) = 3, n (H intersection F) = 2, n (C union H union F) = 42  and n (C intersection H intersection F) = 0.
 
We know:
n (C union H union F) = n(C) + n(H) + n(F) - n(C intersection H) - n(H intersection F) - n(C intersection F) + n (C intersection H intersection F)
 
Substituting the values, we get,
n(C intersection H) = 11
 
But, C = (C intersection H) intersection (C union H')
So, n (C) = n (C intersection H) + n (C intersection H') 
 
[Since, (C intersection H) and (C intersection H') are disjoint sets]
 
Substituting the values, we get
n (C intersection H') = 3
 
Thus, the number of students who play cricket but not hockey is 3.

Answered by  | 2nd Aug, 2012, 10:35: PM

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