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A survey shows that 70% of the Indian like mango where 82% like apple. If x% of Indian like both mango and apples then

(a) x = 52

(b) 52 ≤ x ≤ 70

(c) x = 70

(d) 70 ≤ x ≤ 82

in SETS, RELATIONS AND FUNCTIONS by Expert (11.5k points) | 46 views

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The correct option (b) 52 ≤ x ≤ 70

Explanation:

n(A) = 70 n(B) = 82 n(A ∩ B) = x 

n(A ∪ B) = n(A) + n(B) – n(A ∩ B) 

⇒ n(A ∩ B) = 152 – n(A ∪ B) But n(A ∪ B) ≤ 100

so n(A ∩ B) ≥ 52 

∴ n(A ∩ B) ≤ 70 

∴ 52 ≤ n(A ∩ B) ≤ 70

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