A sample of 200 voters revealed the following about the three candidates A,B and C.28 were in favour of both A and B.98 in favour of A or B but not C.42 in favour of B but not C or A.122 in favour of B or C but not A.64 in favour of C but not A or B.14 in favour of A and C but not B.35 in favour of A but not B or C.Represent that information in a venn diagram.
To represent the information given in a Venn diagram, we need to first identify the number of voters in each region of the diagram.
Let's break down the given information into separate statements:
1. 28 were in favor of both A and B.
2. 98 were in favor of A or B, but not C.
3. 42 were in favor of B, but not C or A.
4. 122 were in favor of B or C, but not A.
5. 64 were in favor of C, but not A or B.
6. 14 were in favor of A and C, but not B.
7. 35 were in favor of A, but not B or C.
Based on this information, we can determine the following:
- A and B only: Since 28 were in favor of both A and B, we place 28 voters in the overlapping region of A and B.
- A only: Since 35 were in favor of A but not B or C, we place 35 voters in region A, outside the overlap with B and C.
- B only: Since 42 were in favor of B but not C or A, we place 42 voters in region B, outside the overlap with A and C.
- C only: Since 64 were in favor of C but not A or B, we place 64 voters in region C, outside the overlap with A and B.
- A and C only: Since 14 were in favor of A and C but not B, we place 14 voters in the overlapping region of A and C.
- B and C only: To determine the number of voters in this region, we need to subtract the number of voters in A and C only (14) from the total number of voters in B or C but not A (122). This gives us 108 voters in the overlapping region of B and C.
Now let's summarize the information in the Venn diagram:
A B
* *
* * *
* *
C
Note: The asterisks (*) represent the number of voters in each region.
By following the given information step by step, we have represented the voter preferences in a Venn diagram.