Question

There are 35 students in art class and 57 students in dance class. Find the number of students who are either in art class or in dance class.
When both art and dance is 12

Answer 1

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Answer 2

Given,

No. of students in art class = 35

No. of students in dance class = 57

No. of students who are in both classes = 12

To find,

No. of students who are either in art class or in dance class.

Solution,

Let A be the set of the students in Art class

and, B is the set of students in Dance class.

So, n(A) = 35

      n(B) = 57

Since 12 students are in both the classes,

⇒ n(A ∩ B) = 12

Therefore, no. of the students in art or dance class will be given by,

n(A ∪ B).

Since we know,

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

              = 35 + 57 - 12

              = 80

∴ No. of students either in art or dance class = 80