Question

10.In a group of persons, 23 like vanilla ice cream, 19 like strawberry ice cream and 8 like both the ice creams. Find(a) the number of persons in the group.(b) the number of persons who like vanilla ice cream only.(c) the number of persons who like strawberry ice cream only.​

Answer 1

Answer:

34,15&11 respectively, Go through following attachment

Answer 2

(a) The number of persons in the group is 34.

(b) The number of people who like vanilla ice cream only is 15.

(c) The number of persons who like strawberry ice cream only is 11.

Given: The number of people liking vanilla = 23,

The number of people liking strawberries = 19,

The number of people liking both = 8,

To Find: (a) the number of persons in the group.

(b) the number of persons who like vanilla ice cream only.

(c) the number of persons who like strawberry ice cream only.​

Solution:

• We know that we can find the total number by the formula,

       n (AUB) = n (A) + n (B) - n (A∩B)                                    ...(1)

• We know that whenever we need to calculate "only" something, we must use the formula,

       n ( A - B ) = A ∩ B' = n (A) - n (A∩B)                                ...(2)

where n ( A - B ) means something present only in A and not in B.

(a) We need to find the number of persons in the group, and we are given n (V) = 23, n(S) = 19, n (V∩S) = 8.

Putting respective values in (1), we get;

        n (VUS) = n (V) + n (S) - n (V∩S)        

   ⇒  n (VUS) = 23 + 19 - 8

   ⇒  n (VUS) = 34

Hence, the number of persons in the group is 34.

(b) We need to find the number of persons who like vanilla ice cream only and we are given, n (V) = 23, n(S) = 19, and n (V∩S) = 8.

So, putting respective values in (2), we get;

          n ( V - S ) = n (V ∩ S') = n (V) - n (V∩S)  

     ⇒  n ( V - S ) = 23 - 8

     ⇒  n ( V - S ) = 15

Hence, the number of people who like vanilla ice cream only is 15.

(c) We need to find the number of persons who like strawberry ice cream only and we are given, n (V) = 23, n(S) = 19, and n (V∩S) = 8.

So, putting respective values in (2), we get;

          n ( S - V ) = n (S ∩ V') = n (S) - n (V∩S)  

     ⇒  n ( S - V ) = 19 - 8

     ⇒  n ( S - V ) = 11

Hence, the number of persons who like strawberry ice cream only is 11.

Compiling the answers we get,

(a) The number of persons in the group is 34.

(b) The number of people who like vanilla ice cream only is 15.

(c) The number of persons who like strawberry ice cream only is 11.

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