Question

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

Answer 1

Let A be the set of students who drink tea, and B be the set of setudents who drink coffee.

We have,

n(U) = 125, n(A) = 80, n(B) = 60, $\mathrm{n}(\mathrm{A}\cap \mathrm{B})=20$

Since,

$\mathrm{n}(\mathrm{A}\cup \mathrm{B})=\mathrm{n}\left(\mathrm{A}\right)+\mathrm{n}\left(\mathrm{B}\right)-\mathrm{n}(\mathrm{A}\cap \mathrm{B})=80+60-20$

$\mathrm{n}(\mathrm{A}\cup \mathrm{B})=120$

So, the number of students who do not drink tea or coffee = 125 $-$ 120 = 5