Question

There are 35 students in art class and 57 students in dance class. Find the number of students
A. who are either in art class or dance class
B. when two classes meet at the same hour
c. when two classes meet at different hours
WITH READABLE SOLUTION

Answer 1

Answer:

A be the set of students in art class

B be the set of students in dance class

n(A) = 35

n(B) = 57

a) When 2 classes meet at different hours and n(A ∩ B) = 12 we have:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 35 + 57 - 12 = 80

b) When two classes meet at the same hour we have A∩B = ∅ that is n(A ∩ B) = 0 and

n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = n(A) + n(B) = 35 + 57 = 92

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Answer 2

Answer:

80

Step-by-step explanation:

Given : 35 Student in art class and 57 in Dance Class  . 12 students are enrolled in both activities

To find : the number of students who are either in dance class or art class

Solution:

Number of Students in Art Class  n(A) = 35

Number of Students in Dance class  n(D) = 57

Number of Students in Art & Dance class Both n(A∩D) = 12

number of students who are either in dance class or art class = n( A U D)

n( A U D)  = n(A) +  n(D)  -  n(A∩D)

=> n( A U D)  = 35 + 57 - 12

=> n( A U D)  = 92 - 12

=> n( A U D)  = 80

80  number of students who are either in dance class or art class