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# In a class of 62 students, 30 students like cricket, 25 students like football and 10 students like both the games. Find the number of students who :(a) Like either cricket or football(b) Like neither cricket nor football

Asked by Topperlearning User 21st September 2016, 10:12 AM

Let U represent the universal set of the class of 62 students.

Therefore, n (U) = 62

Let C represent the set of students who like cricket

Therefore, n(C) = 30

Let F represent the set of students who like football

Therefore, n(F) = 25

Also, F  C = set of students who like both cricket and football

Therefore, n (F  C ) = 10

(i) Let F  C = set of students who like either cricket or football

Therefore, n (F  C) = n (C) + n(F) - n(F  C ) = 30 + 25 - 10 = 45

Hence, no. of students who like either cricket or football = 45

(ii) Students who like neither cricket not football =  n (F  C)' = n (U) - n (F  C) = 62 - 45 = 17

Answered by Expert 21st September 2016, 12:12 PM
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