(i) brands A, B, & C,(ii) brands A or B but not C, (iii) brands B & C but not A, (iv). single brand only?

AAA Plc produces 3 brands A,B %26amp;C of powder milk. In order to determine the marketability of this product some samples were sent out. The result of this exercise, shows that 120 customers liked brand A; 100 customers liked brand B, 110 customers liked brand C, 30 customers liked brands A and B, 25 customers liked brands B and C, 20 customers liked brands A and C and the same number of those customers that liked all three brands also dislike all the brand.


In a sample of 275 customers, how many of them liked

(i) brands A, B, %26amp; C,(ii) brands A or B but not C, (iii) brands B %26amp; C but not A, (iv). single brand only?
10 people liked all the brands as well as hated them.





Use the relation





A U B U C = A + B + C - A∩B - A∩C - B∩C + A∩B∩C





Let the last term be x and A U B U C = 275 - x





Then





275-x = 120 + 100 + 110 - 30 - 25 - 20 +x





gives 275-x = 255+x





Thus x = 10
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