Question

In a survey of 120 consumers conducted in a shopping mall, 80 consumers indicated that they buy Brand A of a certain product, 68 buy Brand B, and 42 buy both brands. How many consumers participating the survey buy:

a) At least one of these brands?
b) Exactly one of these brands?

For a):
Would this translate as n(A U B)

For b):
Would this translate as n(A U Bcomplement) and n(Acomplement U B)

Answer 1

For a , I know that it is 106.
n(A U B) = 80+68-42=106

Answer 2

But I am stuck on part b.
Would it be :
n(A U Bcomplement) = n(a) - n(A ∩ B)
and n (Acomplement U B) = n(b) - n(A ∩ B).
Or does DeMorgan's law apply to sets with complements?

Answer 3

Would it apply in the sense of n(AUBcomplement) = n(AcomplementUB)?