There are 91 eighth-grade students signing up for electives.
Of these 91 students, 68 sign up for the art, 31 sign up for
band, and 18 signed up for both. 10 Students are not signing
up for either art or band.
Let S = {all eighth students}
Let A = {students in Art}
Let B = (students in band)
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A). 81 students

B). 18 students

C). 10 students

Step-by-step explanation:

Let S = {All students of 8th grade} = 91

     A = {Students in Art} = 68

     B = {Students in band} = 31

Part A : A∪B = A + B - A∩B

            A∪B = 68 + 31 - 18

            A∪B = 81

A∪B represents the total number of students enrolled in art and band.

Part B : A∩B = 18

A∩B represents the number of common students enrolled in art and band.

Part C: ~(A∪B) = S - A∪B

           ~(A∪B) = 91 - 81

           ~(A∪B) = 10

~(A∪B) represents the number of students enrolled neither in art nor in band.