Venn Diagram Problem: Survey of 50 Students' Preferences

[korr2221]

In an interview of 50 students,
12 liked Proposition 8 and Proposition 13
18 liked Proposition 8, but not Proposition 5
4 like Proposition 8, Proposition 13 and Proposition 5
25 liked Proposition 8
15 liked Proposition 13
10 liked Proposition 5, but not Proposition 8 or Proposition 13
1 liked Proposition 13 and Proposition 5, but not Proposition 8

a. Show the completed Venn diagram
b. Of those surveyed, how many did not like any of the three propositions?
c. How many liked Proposition 8 and Proposition 5?

Where do I start, can someone give me step by step directions? Thanks

 

[statdad]

Draw as many circles (overlapping) as there are categories
Begin labeling counts where all 3 intersect, then 2 at at time, etc.
Be careful with your counting.

 

[arildno]

To help you a bit more:
As you work yourself "outward" as statdad suggests, set "x", "y" and so on in regions not covered by any explicit statements. These will help you establishing equations you'll probably need to solve.

 

[korr2221]

problem solved. thanks everyone.