Question

Make a Venn Diagram from the following information to answer below question?25 students played soccer 4 boys played soccer and baseball 3 girls played soccer and baseball 10 boys played baseball 4 girls played baseball 9 students played tennis 3 boys played soccer and tennis 3 girls played soccer and tennis 3 boys played baseball and tennis 1 girl played baseball and tennis 1 boy played all three sports 1 girl played all three sports How many students played soccer, but not baseball or tennis?

Answer 1

To find the number of students who played soccer but not baseball or tennis, we need to analyze the given information and use the formula A = (A ∩ B) + (A ∩ C) + (A - A ∩ B ∩ C). Substituting the given values, we find that 32 students played soccer but not baseball or tennis.

Step-by-step explanation:

To determine how many students played soccer but not baseball or tennis, we need to analyze the information given in the Venn diagram provided. Let's label the regions of the Venn diagram:

A represents the set of students who played soccer.

B represents the set of students who played baseball.

C represents the set of students who played tennis.

From the given information, we know that:

• A = 25
• A ∩ B = 4
• A ∩ C = 3
• B = 10
• B ∩ C = 4
• C = 9
• A ∩ B ∩ C = 1

To find the number of students who played soccer but not baseball or tennis, we need to calculate the value of A without the intersection of the other sets. Using the formula:

A = (A ∩ B) + (A ∩ C) + (A - A ∩ B ∩ C),

we can substitute the given values:

A = 4 + 3 + (25 - 1)

A = 32

Therefore, 32 students played soccer but not baseball or tennis.