Question

in a group of 36 people 20 like coffee 22 like tea 3 dislike both find how many like both​

Answer 1

Step-by-step explanation:

Ans=7

Person like both=(15+18)-26=7

Answer 2

Answer:

The number of people who like both coffee and tea is 9.

Step-by-step explanation:

Given the total number of people in a group,  n = 36

the number of people who dislike both coffee and tea is 3.

Therefore, the total group who like either coffee or tea is

$n(C\cup T)=36-3=33$

Given the number of people who like coffee, n(C)=20

Number of people who like tea, n(T)=22

• When the two given sets A and B are finite sets and not disjoint sets,  then the union and intersection sets are finite and both are related through a theorem called inclusion–exclusion principle, given by  

        $n(A\cup B)=n(A)+n(B)-n(A\cap B)$

• where the number of elements in union set, includes n(A) and n(B) and excludes intersection.

Using the formula in the present case,

$n(C\cup T)=n(C)+n(T)-n(C\cap T)$

Substituting the values,

$33=20+22-n(C\cap T)$

$\implies n(C\cap T)=42-33=9$

Thus, the number of people who like both coffee and tea is 9.

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