Question

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

Answer 1

Step-by-step explanation:

i. Let U be the set of students in the hostel, T be the set of students who drink tea and C be the set of students who drink coffee.

n(U) = 125, n(T) = 80, n(C) = 60,

Number of students who drink Tea and Coffee = n(T ∩ C) = 20

ii. n(T ∪ C) = n(T) + n(C) – n(T ∩ C) =

80 + 60 – 20

∴ n(T ∪ C) = 120

∴ 120 students drink tea or coffee

Also, there are 125 students in the hostel.

iii. Number of students who do not drink tea or coffee

= n(U) – n(T ∪ C) = 125 – 120 = 5

∴ 5 students do not drink tea or coffee.

Alternate Method:

Let U be the set of students in the hostel, T be the set of students who drink tea and C be the set of students who drink coffee.

Here drawing will come which I have provided and then write

From Venn diagram, Student who drinks tea or coffee = n(T ∪ C) = 60 + 20 + 40 = 120

∴ The number of students who do not drink tea or coffee = n(U) – n(T ∪ C) = 125 – 120 = 5

∴ 5 students do not drink tea or coffee.

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Answer 2

5 is the correct answer...............