Question

In a group of 24 persons 6 are Indians 12 are doctors 15 chess players one person who is Indian doctor plays chess to Indian doctors don't play chess there are two Indian chess player who are not doctors how many of them were doctors who play chess but not Indians

Answer 1

Answer:

6

Step-by-step explanation:

Let us define the following sets

A: Set representing Indians

B: Set representing Doctors

C: Set representing Chess Players

Then

n(A) = 6

n(B) = 12

n(C) = 15

n(A∪B∪C) = 24

n(A∩B∩C) = 1

n(A∩B)=2

n(A∩C)=2

We have to find n(B∩C)

Using

n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C)

24 = 6 + 12 + 15 - 2 - n(B∩C) - 2 + 1

On solving

n(B∩C) = 6

Answer 2

Answer:

Step-by-step explanation:

Our question is: In a group of 24 persons 6 are Indians 12 are doctors 15 chess players one person who is Indian doctor plays chess to Indian doctors don't play chess there are two Indian chess player who are not doctors.

Our aim is to find how many of them were doctors who play chess but not Indians?

Since we want to find how many of them were doctors who play chess but not Indians, lets organize the information given initially.

We know that:

• 6 are Indians
• 12 are doctors
• 15 are chess players
• 1 is Indian, doctor and plays chess
• 2 are Indian and doctors
• 2 are Indian and play chess

Lets consider m to be the number of people who are doctors and chess players.

Since we want to find how many are doctors and chess players, using the D'Morgan laws, we can see that 24 = 6 + 12 + 15 - m - 2 - 2 + 1.

From here we can get our m and reach our aim.

Then, computing that equation in order to find the variable m, we get m = 6.

Hence, the number of people who were doctors who play chess but not Indians is 6.

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