1.

In a class of 50 students, 30 take Mathematics, 25 take Biology and 15 take both Mathematics and Biology. How many students take neither Mathematics nor Biology?1. 52. 103. 154. 20

Answer» Correct Answer - Option 2 : 10

Given:

The total number of students in a class = 50 

The number of students takes Mathematics = 30

The number of students takes Biology = 25

The number of students take both Mathematics and Biology = 15

Formula used:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B) 

n(A ∪ B)' = n(U) - n(A ∪ B)

where, n(A) = number of elements in A, n(B) = number of elements in B

n(A ∩ B) = number of elements in both A and B, n(A ∪ B) = number of elements in either A or B

n(U) = number of total students

Calculation:

Let the set of total students be U, the set of students takes Mathematics be A

And the set of students takes Biology be C.

According to the question,

n(U) = 50, n(A) = 30, n(B) = 25 and n(A ∩ B) = 15

Now, students take either Mathematics or Biology = n(A ∪ B)

⇒ n(A) + n(B) - n(A ∩ B) 

⇒ 30 + 25 - 15

⇒ 40

So, students take neither Mathematics nor Biology = n(A ∪ B)'

⇒ n(U) - n(A ∪ B)

⇒ 50 - 40

⇒ 10

∴ The students take neither Mathematics nor Biology is 10.


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