Question
or
8 of the students in Kaylee's grade like to drink grapefruit juice. 8 students like to drink cranberry juice, and 4 students like to drink both grapefruit juice and cranberry juice. How many students like to drink cranberry juice but not grapefruit juice?
Hint: Copy and complete the Venn diagram below to help you solve the problem.
I like to drink grapefruit juice
I like to drink cranberry juice
students
Answers
GPT-4o mini
To solve this problem, let's set up the information using a Venn diagram.
1. Let \( A \) represent the set of students who like grapefruit juice.
2. Let \( B \) represent the set of students who like cranberry juice.
From the problem, we have the following information:
- \( |A| = 8 \) (the number of students who like grapefruit juice)
- \( |B| = 8 \) (the number of students who like cranberry juice)
- \( |A \cap B| = 4 \) (the number of students who like both grapefruit juice and cranberry juice)
Now, we want to find how many students like only cranberry juice, which can be represented as \( |B - A| \) (the number of students in set \( B \) but not in set \( A \)).
To find \( |B - A| \), we can use the formula:
\[
|B - A| = |B| - |A \cap B|
\]
Substituting the known values:
\[
|B - A| = 8 - 4 = 4
\]
So, the number of students who like to drink cranberry juice but not grapefruit juice is **4 students**.
In summary:
1. Students who like only grapefruit juice: \( |A| - |A \cap B| = 8 - 4 = 4 \)
2. Students who like only cranberry juice: \( |B| - |A \cap B| = 8 - 4 = 4 \)
3. Students who like both: \( |A \cap B| = 4 \)
Overall, there are:
- 4 students who like only grapefruit juice
- 4 students who like only cranberry juice
- 4 students who like both juices
Thus, the answer to your question is **4 students** who like to drink cranberry juice but not grapefruit juice.
1. Let \( A \) represent the set of students who like grapefruit juice.
2. Let \( B \) represent the set of students who like cranberry juice.
From the problem, we have the following information:
- \( |A| = 8 \) (the number of students who like grapefruit juice)
- \( |B| = 8 \) (the number of students who like cranberry juice)
- \( |A \cap B| = 4 \) (the number of students who like both grapefruit juice and cranberry juice)
Now, we want to find how many students like only cranberry juice, which can be represented as \( |B - A| \) (the number of students in set \( B \) but not in set \( A \)).
To find \( |B - A| \), we can use the formula:
\[
|B - A| = |B| - |A \cap B|
\]
Substituting the known values:
\[
|B - A| = 8 - 4 = 4
\]
So, the number of students who like to drink cranberry juice but not grapefruit juice is **4 students**.
In summary:
1. Students who like only grapefruit juice: \( |A| - |A \cap B| = 8 - 4 = 4 \)
2. Students who like only cranberry juice: \( |B| - |A \cap B| = 8 - 4 = 4 \)
3. Students who like both: \( |A \cap B| = 4 \)
Overall, there are:
- 4 students who like only grapefruit juice
- 4 students who like only cranberry juice
- 4 students who like both juices
Thus, the answer to your question is **4 students** who like to drink cranberry juice but not grapefruit juice.