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Question
A survey was conducted to know the hobby of 220 students of class IX. Out of which 130 students informed about their hobby as rock climbing and 180 students informed about their hobby as sky watching. There are 110 students who follow both the hobbies. Then how many students do not have any of the two hobbies? How many of them follow the hobby of rock climbing only? How many students follow the hobby of sky watching only?
Solution
Let A be the set of students who follow the hobby of rock climbing, and B be the set of students who follow the hobby of sky watching.
We have, n(A) = 130, n(B) = 180, n(A ∩ B) = 110, n(U) = 220
Since,
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
= 130 + 180 - 110
= 200
So, the number of students who do not have any of the two hobbies
= n(U) - n(A ∪ B)
= 220 - 200
= 20
Also, the number of students who follow the hobby of rock climbing only
= n(A) - n(A ∩ B)
= 130 - 110
= 20
And, the number of students who follow the hobby of sky watching only
= n(B) - n(A ∩ B)
= 180 - 110
= 70
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