What will be correct Venn diagram for this solution.

Question

You are given the following information about three sets, A, B and C and their universal set ; n(U)=44,n(A)=23,n(B)=18,n(C)=14, n(A union B)=32, n(B union C)=27,n(A union C)=29 and n(A' intersection B' intersection C')=8.

Draw a venn diagram and put the elements in each region of the diagram.

Answer 1

1. n(U) = a+b+c+d+e+f+g+h = 44

2. n(A) = a+d+e+g = 23

3. n(B) = b+e+f+g = 18

4. n(C) = c+d+f+g = 14

5. n(A union B) = a+b+d+e+f+g = 32

6. n(B union C) = b+c+d+e+f+g = 27

7. n(A union C) = a+c+d+e+f+g = 29

8, n(A’ intersection B’ intersection C’) = h = 8

Start with EQ8: h=8. Then put that into all equations. Now, combine EQ1 and EQ5 mean that c=4. Keep doing this until all values are found.

It helps to subtract equations that have many of the same terms and to plug in known values. Put h=8 in EQ1, then see from the chart below that you may subtract EQ5 to get c=4. The bottom chart is important !!

NOTE: It is usually better to rewrite equations rather than to cross-out values (that gets messy!).

a=9, b=7, c=4, d=5, e=6, f=2, g=3, h=8. Be sure to check these numbers with all equations !!