Question
The Venn diagram above shows a breakdown of a small high school sports program.
Find (Softball/Baseball ∪ Tennis) ∩ (Basketball)'.
Question 2 options:
15
61
3
28
Find (Softball/Baseball ∪ Tennis) ∩ (Basketball)'.
Question 2 options:
15
61
3
28
Answers
GPT-4o mini
To solve for \((\text{Softball/Baseball} \cup \text{Tennis}) \cap \text{(Basketball)}'\) using a Venn diagram, we need to break down the sets involved.
1. **Softball/Baseball**: This set includes all players who play either Softball or Baseball.
2. **Tennis**: This set includes players who play Tennis.
3. **Basketball'**: This represents the set of students who do not play Basketball.
**Step 1: Identify Softball/Baseball ∪ Tennis**
- We combine the numbers from the Softball/Baseball section and the Tennis section of the Venn diagram.
**Step 2: Determine the union of these two sets.**
- Let’s represent the number of players:
- Softball: S
- Baseball: B
- Tennis: T
- The union would include all players from both sports, meaning we sum the unique counts of Softball/Baseball and Tennis.
**Step 3: Identify the complement of Basketball (Basketball')**
- This set includes everyone who is not in the Basketball section of the diagram.
**Step 4: Finally, calculate the intersection**
- We find the intersection of the union found in Step 1 and Basketball' from Step 3. This gives us the number of players who are either in Softball/Baseball or Tennis but not playing Basketball.
Without the specific numbers from the Venn diagram, we cannot compute the exact answer. However, if you provide the counts for each sport from the diagram, I can help complete the calculation!
1. **Softball/Baseball**: This set includes all players who play either Softball or Baseball.
2. **Tennis**: This set includes players who play Tennis.
3. **Basketball'**: This represents the set of students who do not play Basketball.
**Step 1: Identify Softball/Baseball ∪ Tennis**
- We combine the numbers from the Softball/Baseball section and the Tennis section of the Venn diagram.
**Step 2: Determine the union of these two sets.**
- Let’s represent the number of players:
- Softball: S
- Baseball: B
- Tennis: T
- The union would include all players from both sports, meaning we sum the unique counts of Softball/Baseball and Tennis.
**Step 3: Identify the complement of Basketball (Basketball')**
- This set includes everyone who is not in the Basketball section of the diagram.
**Step 4: Finally, calculate the intersection**
- We find the intersection of the union found in Step 1 and Basketball' from Step 3. This gives us the number of players who are either in Softball/Baseball or Tennis but not playing Basketball.
Without the specific numbers from the Venn diagram, we cannot compute the exact answer. However, if you provide the counts for each sport from the diagram, I can help complete the calculation!