Set Theory and Venn Diagrams

The video tutorial explains how to solve a problem involving a survey of pet owners using Venn diagrams. It covers the concepts of set theory, including cardinality and set notation, to determine how many pet owners have only dogs and not cats. The tutorial walks through the calculation process, providing a clear understanding of how to use Venn diagrams to solve similar problems.

How many pet owners were surveyed in total?

• 155

• 8

• 78

• 36

What does the intersection of sets D and C represent in the Venn diagram?

• Owners of only dogs

• Owners of neither dogs nor cats

• Owners of only cats

• Owners of both dogs and cats

What is the cardinality of set D?

• 36

• 78

• 8

• 155

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

• 8

• 28

• 78

• 36

What is the number of elements in set C?

• 28

• 36

• 78

• 8

How many pet owners own a dog but not a cat?

• 78

• 8

• 36

• 28

How many elements are only in set C?

• 8

• 78

• 70

• 28

What is the cardinality of D intersect C complement?

• 28

• 8

• 36

• 78

What is the number of elements in the universal set that are not in D or C?

• 49

• 28

• 155

• 106

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

• 106

• 155

• 49

• 28