Question

In a class of 60 Students 40 like maths, 36 like english and 8 students like maths nor English.How many like both...from set theory
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Answer 1

Answer:

Step-by-step explanation:

n(A)=40,n(B)=36,n(A∩B)=24.

i) The number of students who like only maths.

We will consider the number of students who like only maths as n (only maths). So, we can calculate it as,

n (only maths) =n(A)−n(A∩B)

By substituting the values, we get,

n (only maths) = 40 - 24 = 16.

Hence, we can say there are 16 students who like only maths.

ii) The number of students who like only science.

We will consider the number of students who like only science as n (only science). So, we can calculate it as,

n (only science) =n(B)−n(A∩B)

By substituting the values, we get,

n (only science) = 36 - 24 = 12.

Hence, we can say there are 12 students who like only science.

iii) The number of students who like either maths or science.

We will consider the number of students who like either maths or science as n (either maths or science). So, we can calculate it as,

n (either maths or science) = n (only maths) + n (only science) + n (both science and maths)

By substituting the values, we get,

n (only science) = 16 + 12 + 24 = 52

Hence, we can say there are 52 students who like either maths or science.

iv) The number of students who like neither maths nor science.

We will consider the number of students who like neither maths nor science as n (neither maths nor science). So, we can calculate it as,

n (neither maths nor science) = 60−n(A∪B)

Now, to calculate the value of n(A∪B), we will use the formula, n(A∪B)=n(A)+n(B)−n(A∩B). So, putting the value in the formula, we get,

n(A∪B)=40+36−24⇒n(A∪B)=52

So, by using the value of n(A∪B), we get,

n (neither maths nor science) = 60 - 52 = 8

Hence, we can say there are 8 students who like neither maths nor science.