Answer :
Certainly! Let's go through each part of the problem step-by-step.
### Given Data:
- Total students in the class: [tex]\(\pi\)[/tex]
- Number of students who play football: 6
- Number of students who play title turns: 1
- Number of students who play both games: 5
### Part (a): Illustrate the Venn Diagram
1. Determine the number of students who play only football:
- Students who play football but not title turns are obtained by subtracting those who play both from those who play football.
- Only Football = Total Football - Both Games
[tex]\[ \text{Only Football} = 6 - 5 = 1 \][/tex]
2. Determine the number of students who play only title turns:
- We are given that Students who play title turns is 1. To find those who play only title turns, we subtract those who play both from this total.
- Only Title Turns = Total Title Turns - Both Games
[tex]\[ \text{Only Title Turns} = 1 - 5 = -4 \][/tex]
Since the number of students cannot be negative, this indicates a mistake in the provided numbers. Therefore, we assume it includes those who play both, so the only students playing title turns exclusively would be:
[tex]\[ \text{Only Title Turns} = 1 (including those who play both) \][/tex]
3. Number of Students who play at least one of the games:
- Add the students who play only football, only title turns, and both.
[tex]\[ \text{At least one} = \text{Only Football} + \text{Only Title Turns} + \text{Both} \][/tex]
[tex]\[ \text{At least one} = 1 + (-4) + 5 = 2 \][/tex]
4. Number of Students who play more than one game:
- By definition, this is the number of students who play both games.
[tex]\[ \text{More than one} = 5 \][/tex]
### Part (b): Find the number of students who play at least one or more of the games.
- From our calculations above:
[tex]\[ \text{At least one} = 2 \][/tex]
### Summary of Results
- Total number of students: [tex]\(\pi\)[/tex] (approximately 3.14 rounded for practical purposes).
- Students who play only football: 1
- Students who play only title turns: -4 (which doesn't make sense in real scenarios and suggests an issue with the original data)
- Students who play at least one game: 2
- Students who play more than one game: 5
Given the above analysis, while the calculated results indicate a possible error in provided numbers, strictly adhering to them yields:
- Visualization would show 1 student in "Only Football," certain context assumptions with negative impact clarified data, 2 for "at least one," and 5 for "both." A practical context would be 0 or non-negative realistic validation.
### Given Data:
- Total students in the class: [tex]\(\pi\)[/tex]
- Number of students who play football: 6
- Number of students who play title turns: 1
- Number of students who play both games: 5
### Part (a): Illustrate the Venn Diagram
1. Determine the number of students who play only football:
- Students who play football but not title turns are obtained by subtracting those who play both from those who play football.
- Only Football = Total Football - Both Games
[tex]\[ \text{Only Football} = 6 - 5 = 1 \][/tex]
2. Determine the number of students who play only title turns:
- We are given that Students who play title turns is 1. To find those who play only title turns, we subtract those who play both from this total.
- Only Title Turns = Total Title Turns - Both Games
[tex]\[ \text{Only Title Turns} = 1 - 5 = -4 \][/tex]
Since the number of students cannot be negative, this indicates a mistake in the provided numbers. Therefore, we assume it includes those who play both, so the only students playing title turns exclusively would be:
[tex]\[ \text{Only Title Turns} = 1 (including those who play both) \][/tex]
3. Number of Students who play at least one of the games:
- Add the students who play only football, only title turns, and both.
[tex]\[ \text{At least one} = \text{Only Football} + \text{Only Title Turns} + \text{Both} \][/tex]
[tex]\[ \text{At least one} = 1 + (-4) + 5 = 2 \][/tex]
4. Number of Students who play more than one game:
- By definition, this is the number of students who play both games.
[tex]\[ \text{More than one} = 5 \][/tex]
### Part (b): Find the number of students who play at least one or more of the games.
- From our calculations above:
[tex]\[ \text{At least one} = 2 \][/tex]
### Summary of Results
- Total number of students: [tex]\(\pi\)[/tex] (approximately 3.14 rounded for practical purposes).
- Students who play only football: 1
- Students who play only title turns: -4 (which doesn't make sense in real scenarios and suggests an issue with the original data)
- Students who play at least one game: 2
- Students who play more than one game: 5
Given the above analysis, while the calculated results indicate a possible error in provided numbers, strictly adhering to them yields:
- Visualization would show 1 student in "Only Football," certain context assumptions with negative impact clarified data, 2 for "at least one," and 5 for "both." A practical context would be 0 or non-negative realistic validation.
