Answer :

Given: n(A) = 130, n(B) = 180 and n (A ∩ B) = x = 110

Total number of students = 220

n(A) = number of students whose hobby is rock climbing

n(B) = number of students whose hobby is sky watching

n (A ∩ B) = number of students whose hobby is both

n (A ∪ B) = number of students whose hobby is either rock climbing or sky watching

As we know, n (A ∪ B) = n(A) + n(B) - n (A ∩ B)

⇒ n (A ∪ B) = 130 + 180 - 110

⇒ n (A ∪ B) = 310 - 110

⇒ n (A ∪ B) = 200

Then,

(i) The number of students who do not have any of the two hobbies

= 220– 200

= 20

(ii) The number of students whose hobby is rock climbing

= 130– 110

= 20

(iii) The number of students whose hobby is sky watching

= 180– 110

= 70

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