Using Venn Diagrams for Surveys

In-Class Problem

President Realign does a survey of seventy of her loyal supporters and discovers the following opinions on three issues:

40 want to improve auto mileage (A) 37 want to reduce global warming (G)

19 want to reduce prison populations (P) 10 want A and P

8 want A and G 15 want G and P

3 want all three 11 want none of the three

Draw a Venn diagram to illustrate this – showing all calculations – and use it to decide whether the President might benefit from a math class.

Homework Problems

1) Given the sets A = {1, 2, 3, 4, 5, 6, 7} B = {2, 4, 6, 8, 10, 12} find

a) n(A) and n(B) b) A intersect B and A union B

c) Can you calculate the complement of A ? Explain

2) A survey of country western songs produces the following information about the common themes of love, prison and trains.

11 songs about a traindriver who was in prison and in love

14 about a prisoner in love

31 about people in love

17 about a traindriver in love

4 about a traindriver in prison but not in love

1 about a prisoner who is not in love and does not drive a train

19 about people not in prison, not in love and who don’t drive a train

17 about traindrivers who are not in prison.

Draw a Venn diagram, showing all steps, explanations and calculations, and use it to find how many songs were surveyed.