i. Let U be the set of students of class IX,
R be the set of students who follow the hobby of rock climbing and
S be the set of students who follow the hobby of sky watching.
∴ n (U) = 220, n (R) = 130, n (S) = 180,
110 students follow both the hobbies
∴ n (R ∩ S) = 110
ii. n(R ∪ S) = n (R) + n (S) – n (R ∩ S)
= 130 + 180 – 110
∴ n (R ∪ S) = 200
∴ 200 students follow the hobby of rock climbing or sky watching.
iii. Total number of students = 220.
Number of students who do not follow the hobby of rock climbing or sky watching
= n (U) – n (R ∪ S)
= 220 – 200 = 20
iv. Number of students who follow the hobby of rock climbing only
= n (R) – n(R ∩ S) = 130 – 110 = 20 v.
v. Number of students who follow the hobby of sky watching only
= n (S) – n (R ∩ S) = 180 – 110 = 70
Alternate Method:
Let U be the set of students of class IX, R be the set of students who follow the hobby of rock climbing and S be the set of students who follow the hobby of sky watching.
From the Venn diagram
i. Students who follow the hobby of rock climbing or sky watching = n(R ∪ S) = 20 + 110 + 70 = 200
ii. Number of students who do not follow the hobby of rock climbing or sky watching
= n (U) – n(R ∪S) = 220 – 200 = 20
iii. Number of students who follow the hobby of rock climbing only
= n (R) – n(R ∩S) = 130 – 110 = 20
iv. Number of students who follow the hobby of sky watching only
= n (S) – n (R ∩ S)
= 180 – 110
= 70