Q2 of 43 Page 16

In a hostel there are 125 students, out of which 80 drink tea, 60 drink coffee and 20drink tea and coffee both. Find the number of students who do not drink tea or coffee.

Given: n(A) = 80, n(B) = 60 and n (A ∩ B) = x = 20

Total number of students = 125


n(A) = number of students who drink tea


n(B) = number of students who drink coffee


n (A ∩ B) = number of students who drink both tea and coffee


n (A ∪ B) = number of students who drink either tea or coffee


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


⇒ n (A ∪ B) = 80 + 60 - 20


⇒ n (A ∪ B) = 140 - 20


⇒ n (A ∪ B) = 120


Then, the number of students who do not drink tea or coffee = 125 – 120


= 5


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