Venn Diagrams with 3 Circles

Summary

This lesson teaches how to complete Venn diagrams involving three sets. Using two examples—sports and pets—it explains how to calculate and fill in overlaps and individual totals. The first example discusses 30 students and their involvement in three sports: basketball, football, and tennis, while the second explores pet ownership with categories for dogs, cats, and rabbits. The script guides viewers through determining the correct number of individuals in each section of the diagram, ensuring the totals match the overall group size. This exercise demonstrates how Venn diagrams visually represent intersections of multiple categories.

Takeaways

• 😀 Venn diagrams are used to visualize the overlap between different groups or sets, such as people who play different sports or own various pets.
• 😀 When creating a Venn diagram, it's important to start by filling in the overlap of all sets (e.g., all three sports or pets).
• 😀 For each pair of overlapping circles, make sure to adjust the numbers to reflect the total amount given (e.g., 10 people play both basketball and tennis).
• 😀 The numbers in the individual circles (such as basketball, football, and tennis) should add up to the total number of people who play each sport.
• 😀 In order to complete a Venn diagram, the total of all numbers in and outside the circles must match the overall number of subjects being surveyed (e.g., 30 students or 100 pet owners).
• 😀 For sports, 7 people play all three sports (basketball, football, and tennis), and this number is placed in the center of the diagram.
• 😀 After placing the number for all three sports, adjust the overlapping sections for each pair of sports, ensuring the numbers add up correctly to the total number given for each overlap.
• 😀 The process involves cross-checking the numbers for each section of the Venn diagram to ensure they add up to the overall totals (such as 30 for the sports diagram).
• 😀 For the pets Venn diagram, similar logic applies, with students owning different combinations of dogs, cats, and rabbits, and the total numbers must match the given values (60 dogs, 32 cats, 18 rabbits).
• 😀 Students who do not belong to any group (either in sports or pets) are placed outside the circles to account for those not included in any of the overlapping categories.

Q & A

What is the total number of students surveyed in the first Venn diagram example?

A total of 30 students were surveyed about which sports they play.

How many students play all three sports: basketball, football, and tennis?

Seven students play all three sports.

How is the overlap between basketball and tennis calculated in the diagram?

Ten students play both basketball and tennis in total. Since seven play all three sports, three additional students are placed in the basketball–tennis overlap region.

How many students play both basketball and football?

Eleven students play both basketball and football. Since seven already play all three sports, four more are added to this overlap.

How many students play both football and tennis?

Nine students play both football and tennis, so after accounting for the seven who play all three, two more are added to that overlap region.

How many students play only basketball?

The basketball circle must total 20 students. After subtracting the overlapping numbers (3 + 7 + 4 = 14), six students play only basketball.

How many students do not play any of the three sports?

Two students do not play basketball, football, or tennis. They are placed outside all circles.

In the pets example, how many people own all three pets: dogs, cats, and rabbits?

Three people own all three pets.

How many people have both a dog and a cat but not necessarily a rabbit?

Twenty-one people have both a dog and a cat in total. Since three have all three pets, eighteen more are placed in the dog–cat overlap.

How many people do not own any of the three pets?

Twenty-five people do not own a dog, cat, or rabbit. They are placed outside the Venn diagram.

What is the total number of people in the pet ownership survey?

The total is 100 people.

What is the purpose of filling out the overlaps first when completing a Venn diagram?

Filling out the overlaps first ensures that shared quantities are correctly accounted for, avoiding double counting when completing totals for each individual set.

What is the main difference between the two examples in the lesson?

The first example deals with students playing sports, while the second involves people owning pets. Both demonstrate how to fill a three-circle Venn diagram using given totals and overlaps.