In a recent survey of $100$ women, the following information was gathered: $54$ use shampoo A. $52$ use shampoo B. $35$ use shampoo C. $22$ use shampoos A and B. $18$ use shampoos A and C. $13$ use shampoos B and C. $12$ use all three. Name the three sets in this survey A , B , and C . Use the figure (with Regions I through VIII) to answer the question.
A) A = {women who use shampoo B } B = {women who use shampoos A and C} C = {women who use all three}
B) A = {women who use shampoo A} B = {women who use shampoo B} C = {women who use shampoo C}
C) A = {women who use shampoo A, but not B or C} B = {women who use shampoo B, but not A or C} C = {women who use shampoo C, but not A or B}
D) A = {women who use shampoo A, but not B and C} B = {women who use shampoo B, but not A and C} C = {women who use shampoo A, but not B and C}
E) A = {women who use shampoo A, but not B} B = {women who use shampoo B, but not A} C = {women who use shampoo C, but not A}

Question

In a recent survey of $100$ women, the following information was gathered: $54$ use shampoo A. $52$ use shampoo B. $35$ use shampoo C. $22$ use shampoos A and B. $18$ use shampoos A and C. $13$ use shampoos B and C. $12$ use all three. Name the three sets in this survey A , B , and C . Use the figure (with Regions I through VIII) to answer the question. 
A) A = {women who use shampoo B } B = {women who use shampoos A and C} C = {women who use all three} 
B) A = {women who use shampoo A} B = {women who use shampoo B} C = {women who use shampoo C} 
C) A = {women who use shampoo A, but not B or C} B = {women who use shampoo B, but not A or C} C = {women who use shampoo C, but not A or B} 
D) A = {women who use shampoo A, but not B and C} B = {women who use shampoo B, but not A and C} C = {women who use shampoo A, but not B and C} 
E) A = {women who use shampoo A, but not B} B = {women who use shampoo B, but not A} C = {women who use shampoo C, but not A}

Quizplus · Accepted Answer

The sets A, B, and C are defined by the shampoos used. The information given in the survey indicates that 54 women use shampoo A, 52 women use shampoo B, and 35 women use shampoo C. The sets A, B, and C should be defined by these numbers. Choice B correctly defines the sets A, B, and C based on the given numbers, as follows:

A = {women who use shampoo A}
B = {women who use shampoo B}
C = {women who use shampoo C}

The additional information about overlaps between the sets can be used to determine the sizes of the intersections of the sets. For example, the fact that 22 women use shampoos A and B means that the intersection of A and B has 22 elements. Similarly, the fact that 12 women use all three shampoos means that the intersection of A, B, and C has 12 elements.

In a Recent Survey Of 100100100 Women, the Following Information Was Gathered

In a Recent Survey Of $100$ Women, the Following Information Was Gathered