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. Find

When two classes meet at different hours and 12 students are enrolled in both activities. ( 2marks)

When two classes meet at the same hour. ( 2 marks)​

Answer 1

a. 80 students

b. 92 students

Explanation:

Represent arts students with A and Dance students with D.

So, we have,

n(A) = 35

n(D) = 57

Required

Determine n(A or D)

Solving (a):

Here, we have:

n(A and D) = 12

n(A or D) is calculated as thus:

n(A or D) = n(A) + n(D) - n(A and D)

n(A or D) = 35 + 57 - 12

n(A or D) = 80

b. From the given details

n(A and D) = 0 because both students are not mixed up as in (a) above

Using the same formula as (a).

n(A or D) = n(A) + n(D) - n(A and D)

n(A or D) = 35 + 57 - 0

n(A or D) = 92