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.(by venn diagram ) ​

Answer 1

Step-by-step explanation:

Aswer:-

Given :-

• total nnumber of students are 125.
• out of which 80 drink tea, 60 drink coffee and 20 drink tea and coffee both.

To find:-

• the number of students who do not drink tea or coffee.

Solution:-

$i. \: Let \: \: U \: \: be \: \: the \: \: set \: \: of \: \: students \: \\ in \: \: the \: \: hostel$

$T \: be \: the \: set \: of \: students \: who \: drink \: tea \: \: and \\ C \: be \: the \: set \: of \: students \: who \: drink \: coffee. \:$

$n(U) \: = \: 125, n(T) \: = \: 80, n(C) \: = \: 60,$

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

$ii. \: n(T ∪ C)m \: = \: n(T) \: + \: n(C) \: – \: n(T ∩ C)$

$= \: 80 \: + \: 60 \: – \: 20$

$∴ \: n(T ∪ C) \: = \: 120$

$∴ \: 120 \: students \: drink \: tea \: or \: coffee \:$

$Also, \: there \: are \: 125 \: students \: in \: the \: hostel.$

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

$= \: n(U) \: – \: n(T ∪ C) \: = \: 125 \: – \: 120 \: = \: 5$

$∴ 5 \: students \: do \: not \: drink \: tea \: or \: coffee.$