Question

In a survey of 60 people,it was found that 25 people like coffee,26 people like tea,24 people like milk,9 people like both coffee and
milk,11 people like both coffee and tea,8 people like both tea and milk,and 3 people like all.Find
1)the number of people who like coffee and tea but not milk
2)the number of people who like none of these

Answer 1

N = 60
If you know Venn diagrams, then do that using circular areas for sets.  Let U denote the union symbol.  ∧ denotes intersection.  see diagram.

Coffee C = 25          Tea T = 26              Milk M = 24
C  ∧  M = 9            C  ∧  T = 11            T ∧ M = 8          C  ∧  T  ∧  M  = 3

1)    (C ∧ T) -  M  =   (C∧ T) -  (C ∧ T∧ M)  = 11 - 3 = 8
2)  add the number of persons in each colored region ie., each inside some circle.
   that gives the number of persons who like  some drink.  That comes to 50.

   the number of people who dont  like any drink = 60  -  50 = 10

Answer 2

Answer:

N = 60

If you know Venn diagrams, then do that using circular areas for sets.  Let U denote the union symbol.  ∧ denotes intersection.  see diagram.

Coffee C = 25          Tea T = 26              Milk M = 24

C  ∧  M = 9            C  ∧  T = 11            T ∧ M = 8          C  ∧  T  ∧  M  = 3

1)    (C ∧ T) -  M  =   (C∧ T) -  (C ∧ T∧ M)  = 11 - 3 = 8

2)  add the number of persons in each colored region ie., each inside some circle.

  that gives the number of persons who like  some drink.  That comes to 50.

  the number of people who dont  like any drink = 60  -  50 = 10