of the 11 girls in class:
6 dislike Trevor(T),
5 Dislike Bryce(B),
8 Dislike Drake(D),
3 Dislike T and B,
5 Dislike T and D,
4 Dislike B and D
only Sue-Ellen is friends with all 3,
place students in Venn Diagram and Find the Number and Describe?
To solve this problem, we can use a Venn diagram to represent the relationships between the girls and the boys (Trevor, Bryce, and Drake) in the class.
First, draw three overlapping circles to represent each boy (T, B, and D). Label the circles accordingly.
Next, fill in the numbers according to the given information:
- 6 girls dislike Trevor (T), so write "6" in the region that overlaps with the T circle.
- 5 girls dislike Bryce (B), so write "5" in the region that overlaps with the B circle.
- 8 girls dislike Drake (D), so write "8" in the region that overlaps with the D circle.
- 3 girls dislike both Trevor and Bryce (T and B), so write "3" in the region where the T and B circles overlap.
- 5 girls dislike both Trevor and Drake (T and D), so write "5" in the region where the T and D circles overlap.
- 4 girls dislike both Bryce and Drake (B and D), so write "4" in the region where the B and D circles overlap.
- Lastly, only Sue-Ellen is friends with all three boys, so write "1" in the region where all three circles overlap.
Now, we can count the numbers in each segment of the Venn diagram to find the number of girls in each category and describe it:
- The segment where only Trevor is disliked has 6 girls.
- The segment where only Bryce is disliked has 5 girls.
- The segment where only Drake is disliked has 8 girls.
- The segment where both Trevor and Bryce are disliked has 3 girls.
- The segment where both Trevor and Drake are disliked has 5 girls.
- The segment where both Bryce and Drake are disliked has 4 girls.
- The segment where all three boys are disliked has 1 girl.
- The segment where none of the boys are disliked, which represents Sue-Ellen, has 1 girl.
Therefore, the numbers can be summarized as follows:
- 6 girls dislike Trevor only.
- 5 girls dislike Bryce only.
- 8 girls dislike Drake only.
- 3 girls dislike Trevor and Bryce.
- 5 girls dislike Trevor and Drake.
- 4 girls dislike Bryce and Drake.
- 1 girl dislikes all three boys (Sue-Ellen).
- 1 girl is friends with all three boys (Sue-Ellen).