in a group of 80people, 40like indian food, 36like chinese food and 27 do not like any of these foods. draw venn diagram to find (i) how many like both kind of food? (ii) how many like only indian food? (iii) how many like only the chinese food?
Answers
Step-by-step explanation:
T = Tea
C = Coffee
n means number
n(T) = 30
n(C) = 20
Universal = 50
n(T U C)' = 6 , T union C complement (people who like to drink neither)
Let n(T Π C) i.e. T intersection C (People who like to drink both) = x
n(T) + n(C) - n(T Π C) + n(T U C)' = 50
30 + 20 - x + 6 = 50
56 - x = 50
- x = 50 - 56
-x = -6
x = 6
Therefore people who like to drink BOTH Tea and Coffee are 6.
People who drink coffee = 20
Thus, People who ONLY drink coffee = 20 - 6 = 14 people
I've attached an image with diagram below for better understanding.
Answer:
Let’s solve this using a venn diagram.
T = Tea
C = Coffee
n means number
n(T) = 30
n(C) = 20
Universal = 50
n(T U C)' = 6 , T union C complement (people who like to drink neither)
Let n(T Π C) i.e. T intersection C (People who like to drink both) = x
n(T) + n(C) - n(T Π C) + n(T U C)' = 50
30 + 20 - x + 6 = 50
56 - x = 50
- x = 50 - 56
-x = -6
x = 6
Therefore people who like to drink BOTH Tea and Coffee are 6.
People who drink coffee = 20
Thus, People who ONLY drink coffee = 20 - 6 = 14 people
I've attached an image with diagram below for better understanding