Step-by-step explanation:
To create the Venn diagram, follow these steps:
1. Define Sets:
- Let A represent the students enrolled in Algebra.
- Let S represent the students who play sports.
2. Write the given information:
- Total number of students, n(U) = 500
- Number of students enrolled in Algebra, n(A) = 125
- Number of students who play sports, n(S) = 257
- Number of students enrolled in both Algebra and sports, n(A ∩ S) = 52
3. Calculate number of students in each groups:
[tex]\bullet\ \text{Students only in algebra: $n_o(A)=n(A)-n(A\cap S)=125-52=73$}[/tex]
[tex]\bullet\ \text{Students only in sports: $n_o(S)=n(S)-n(S\cap A)=257-52=205$}[/tex]
[tex]\bullet\ \text{Students in both Algebra and sports: $n_o(A\cap S)=52$}[/tex]
[tex]\bullet\ \text{Students in neither Algebra nor sports: $n_o(AUS)'=n(U)-n(AUS)$}[/tex]
[tex]\text{First, we need to find $A\cup S$ using the formula:}\\n(AUS)=n_o(A)+n_o(S)+n(A\cap S)=73+205+52=330[/tex]
[tex]\text{Therefore, $n(A\cup S)'=500-330=170$}[/tex]
4. Venn Diagram Data:
- Students only in Algebra: 73
- Students only in sports: 205
- Students in both Algebra and sports: 52
- Students in neither Algebra nor sports: 170
