Pet Ownership and Set Theory

The video tutorial explains how to solve a problem involving pet ownership using a Venn diagram. It begins with a survey of 120 pet owners, detailing how many own dogs, cats, or both. The tutorial uses set notation and cardinality to determine how many pet owners own neither a dog nor a cat. By calculating the elements in each set and their intersections, the tutorial concludes that 25 pet owners own neither a dog nor a cat.

How many pet owners were surveyed in total?

• 150

• 120

• 100

• 200

What is the purpose of using a Venn diagram in this problem?

• To visualize the number of pet owners

• To calculate the total number of pets

• To determine the overlap between dog and cat owners

• To find the average number of pets per owner

What does the cardinality of a set represent?

• The sum of all elements

• The size of the largest element

• The number of elements in the set

• The type of elements in the set

How many pet owners own both a dog and a cat?

• 9

• 7

• 5

• 3

What is the number of pet owners who own only a cat?

• 99

• 94

• 89

• 84

How many pet owners own only a dog?

• 6

• 7

• 5

• 4

What is the formula used to find the number of pet owners who own neither a dog nor a cat?

• Cardinality of D intersect C

• Cardinality of P minus D union C

• Cardinality of D union C

• Cardinality of P plus D union C

How many pet owners own neither a dog nor a cat?

• 15

• 30

• 20

• 25

What is the total number of elements accounted for in sets D and C?

• 85

• 100

• 90

• 95

What does the complement of D union C represent in this context?

• Owners of both dogs and cats

• Owners of only cats

• Owners of only dogs

• Owners of neither dogs nor cats