Question

there are 30 teachers who teach mathematics and science in a school.of these,14 teach mathematics and 8 teach both.how many teach science

Answer 1

8 teachers teach only science

Answer 2

No.of teachers who teach only Science is 24.

Given :

No.of teachers who teach mathematics and science in a school = 30

No.of teachers who teach mathematics = 14

No.of teachers who teach both = 8

To find :

No.of teachers who teach science

Solution :

Let set A be the ones who teach mathematics

Let set B be the ones who teach science

Therefore, n(A) = 14

n(B) = ?

n(A U B) = no.of teachers who teach either maths or science = 30

n( A ∩ B) = no.of teachers who teach both maths and science = 8

We know,

n( A U B ) = n(A) + n(B) - n( A ∩ B)

=> 30 = 14 + n(B) - 8

=> 30 - 14 + 8 = n(B)

=> n(B) = 24

Hence, no.of teachers who teach only Science is 24.

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