Understanding Sets and Venn Diagrams

The video tutorial explains how to determine the number of elements in the intersection of two sets, A and B, using a Venn diagram. Set A contains 42 elements, set B contains 23 elements, and the union of both sets contains 55 elements. By subtracting the number of elements in set A from the union, the number of elements only in set B is found. This leads to the calculation of the intersection, which contains 10 elements. The tutorial concludes by verifying the results and demonstrating the solution using the cardinality formula.

What is the total number of elements in either set A or set B?

• 10

• 55

• 23

• 42

How many elements are there in set A?

• 10

• 55

• 42

• 23

What is the number of elements in set B?

• 55

• 42

• 23

• 10

What is the formula used to find the number of elements in the intersection of two sets?

• Number of elements in A + Number of elements in B

• Number of elements in A union B - Number of elements in A

• Number of elements in A union B + Number of elements in B

• Number of elements in A - Number of elements in B

How many elements are only in set B?

• 42

• 23

• 13

• 10

How many elements are in the intersection of sets A and B?

• 42

• 13

• 10

• 23

How many elements are only in set A?

• 42

• 13

• 10

• 32

What is the sum of elements only in A, only in B, and in the intersection?

• 42

• 55

• 10

• 23

What is the cardinality formula used for?

• Determining the intersection of two sets

• Calculating the union of two sets

• Verifying the total number of elements in a union

• Finding the number of elements in a single set

What is the final answer to the question of how many elements sets A and B have in common?

• 42

• 23

• 10

• 13