We have a class of 31 students.
Set A is the set of people who ate an Apple at breakfast. Set A contains 20 students.
Set B is the set of people who ate a Banana at breakfast. Set B contains 10 students.
The number of students in {A ∩ B} is 2.
Assign student counts appropriately for this Venn diagram:
# of students in the area of overlap
# of students in the half-moon labeled A
# of students in the half-moon labeled B
# of students in the box but not inside either circle
To assign student counts to different parts of the Venn diagram, we need to analyze the given information step by step.
1. The number of students in {A ∩ B} is 2.
This means that there are 2 students who ate both an apple and a banana for breakfast. So, the area of overlap between sets A and B should have 2 students.
2. Set A contains 20 students.
This means that there are 20 students who ate an apple for breakfast. So, the half-moon labeled A should have 20 students.
3. Set B contains 10 students.
This means that there are 10 students who ate a banana for breakfast. So, the half-moon labeled B should have 10 students.
4. The number of students in the box but not inside either circle.
To find the number of students in this region, we can subtract the total number of students in sets A and B along with the overlapping region from the total number of students in the class.
Total number of students in the class = 31
Students in the overlapping region {A ∩ B} = 2
Students in set A = 20
Students in set B = 10
So, the number of students in the box but not inside either circle would be:
31 - (2 + 20 + 10) = 31 - 32 = -1
Since we cannot have a negative count, it seems like there might be an error in the given information. Please double-check the values provided for set A, set B, and the intersection {A ∩ B}, as it seems those numbers do not add up correctly.