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

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Step-by-step explanation:

Let

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

5+2x=a

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