1. Let U= {1, 2, 3, 4, 5, 6, 7, 8,a,b,c,d,e}. If A= {1, 2,a,e} and B= {1, 2, 3, 4,a,b,c}, find the following.

(a)

n(A^c)

(b)

n(AB^c)

(c)

n(AB^c)

(d)

n(A^cB^c)

2. In a study of factors that influence brand switching by a certain demographic, the following factors were identified as being significant as judged by the responses of the 439 participants in the survey.

1:	Better price
2:	Friend's recommendation
3:	Seeing others use it
4:	Interesting packaging
5:	Buzzpeople talking about the brand
6:	An advertisement
7:	Press stories
8:	Entertainer/sports celebrity endorsement

The results of the survey follow.

Factor	1	2	3	4	5	6	7	8
Respondents (%)	68.8	60.2	22.6	20.6	16.8	16.8	14.7	6.7

Let A denote the set of factors that had a response greater than 20%, let B denote the set of factors that had a response between 15% and 25%, and let C denote the set of factors that had a response less than 25%. Find the following.(a)

n(A), n(B), n(C)

n(A) =
n(B) =
n(C) =

(b)

n(A B)

(c)

n(A^c C)

(d)

n(A B^c)

(e)

n(A^c C^c)

(f)

n[(A B) C]

3. In a survey,170consumers were asked about their buying preferences concerning a product that is sold in the market under three labels. The results were as follows.14buy only those sold under label A. 24buy only those sold under label B. 25buy only those sold under label C. 13buy only those sold under labels A and B. 10buy only those sold under labels A and C. 13buy only those sold under labels B and C. 9buy the product sold under all three labels.How many of the consumers surveyed buy the product sold under (a) At least one of the three labels? consumers (b) Labels A and B but not C? consumers (c) Label A? consumers (d) None of these labels? consumers