Question

In a group of 50 people, two tests were conducted, one for diabetes and one for blood pressure. 30 people were diagnosed with diabetes and 40 people were diagnosed with high blood pressure. What is the minimum number of people who were having diabetes and high blood pressure?

- No copied answers please
- Well explanation needed ​

xD​

Answer 1

Answer:

Let A be the set containing people diagnosed with diabetes and

B be the set containing people diagnosed with blood pressure

We know the set formula :

n(A U B) + n(A n B) = n(A) + n(B)

n(A n B) = x are people having both

n(A U B) are total people

n(A) is people having diabetes and n(B) is people having blood pressure

:. 50 + x = 40 + 30

:. x = 70 - 50

:. x = 20

Thus, the minimum people having both is 20

Answer 2

SOLUTION

Concept:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

Calculation:

Let, A be the number of people tested for diabetes and B be the number of people tested for blood pressure and there are 50 people tested either for diabetes or blood pressure 

So, n(A) = 30, n(B) = 40, n(A ∪ B) = 50

n(A ∩ B) = ?

We know,

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

⇒ n(A ∩ B) = 30 + 40 - 50

= 20

Hence, option (3) is correct.