Answer to Question #139418 in Discrete Mathematics for Adolph Owusu Kwabena

Question

In a a class of 80 students 53 study Art 60 study Biology 36 study art and Biology 34 study art and Chemistry 6 study Biology only and 18 study biology but not chemistry. How many students study art only and how many students study chemistry

Answer 1

A + B + C + D + E + F + G = 80 (1)

A + D + G + F =53 (2)

B + F+ G + E = 60 (3)

D+G =34 (4)

F+G = 36 (5)

B = 6 (6)

B + F = 18 (7)

We need to find A and (C + D + E + G).

(7) - (6): F=12

(5): G = 36 - F = 36 -12 = 24

(4): D = 34 - G =34 - 24 = 10

(3): E = 60 - B - F - G = 60 - 6 - 12 - 24 = 18

(1) - (3): A + C + D = 20

(2) - last result: G + F - C = 33 => C = 24 + 12 - 33= 3

Then

C+ D + E + G = 3 + 10 + 18 + 24 = 55.

(1) A + B + F = 80 - 55 =25

A = 25 - F - B = 25 - 12 - 6 = 7.

Answer: art only - 7, chemistry - 55.