There are 150 people at an international medical conference,40 are African, 70 are women and 110 are doctors. 12 of the women are African, 46 of the doctors are women and 31 of the Africans are doctors. If 5 of the African men are not doctors.(i) how many of the African women are doctors?(ii) how many of the men are neither African nor doctor?
To answer these questions, we need to break down the information provided and analyze the different categories of people at the conference.
Let's define the variables:
A = number of Africans
W = number of women
D = number of doctors
Given information:
A = 40 (40 people are African)
W = 70 (70 people are women)
D = 110 (110 people are doctors)
We are also given the following additional information:
12 of the women are African (12 women are African)
46 of the doctors are women (46 doctors are women)
31 of the Africans are doctors (31 Africans are doctors)
5 of the African men are not doctors (5 African men are not doctors)
Now, let's solve the questions step by step:
(i) How many of the African women are doctors?
To find the number of African women who are doctors, we need to find the intersection of Africans, women, and doctors.
Firstly, let's find the number of African women:
African women = 12 (number of women who are African)
Next, let's find the number of women who are doctors:
Women doctors = 46 (number of doctors who are women)
To find the number of African women who are doctors, we need to find the intersection of African women and women doctors:
African women who are doctors = African women ∩ women doctors
Since we don't have the exact information about the intersection of African women and women doctors, we need to use the given information to calculate it.
The total number of African doctors is given as 31. However, since we know that 5 African men are not doctors, we can subtract these from the count of African doctors. Therefore, the number of African women who are doctors will be:
African women who are doctors = 31 - 5 = 26
So, there are 26 African women who are doctors.
(ii) How many of the men are neither African nor doctors?
To find the number of men who are neither African nor doctors, we need to find the complement of African men and doctor.
Firstly, let's find the number of African men:
African men = A - African women = 40 - 12 = 28
Next, let's find the number of all doctors:
All doctors = D
To find the number of men who are neither African nor doctors, we need to subtract the African men who are doctors from the total count of African men:
Men who are neither African nor doctors = African men - African men who are doctors
Since the number of African men who are doctors is not given explicitly, we can calculate it using the given information:
African men who are doctors = African men - (31 - 5) = 28 - 26 = 2
Therefore, there are 2 men who are neither African nor doctors.
In summary:
(i) There are 26 African women who are doctors.
(ii) There are 2 men who are neither African nor doctors.