Understanding Venn Diagrams and Set Operations

The video tutorial explains how to find the number of elements in the set A ∩ C ∩ B' using a Venn diagram. It begins by introducing the universal set and subsets A, B, and C. The tutorial then demonstrates how to identify elements in different regions of the Venn diagram, including those in the universal set but not in A, B, or C. Finally, it calculates the intersection of A and C, and B complement, concluding with a review of the problem without using a Venn diagram.

What is the universal set in this example?

• Whole numbers 1 through 15

• Whole numbers 1 through 30

• Whole numbers 1 through 20

• Whole numbers 1 through 10

Which elements are common to sets A, B, and C?

• 8, 9, 10

• 7, 8, 9

• 8, 9, 15

• 9, 10, 15

Which element is only in sets A and B?

• 12

• 13

• 11

• 10

Which elements are only in sets B and C?

• 5, 6, 14

• 4, 5, 14

• 4, 6, 14

• 4, 6, 15

Which elements are only in sets A and C?

• 12, 13

• 11, 12

• 11, 13

• 10, 11

Which element is only in set A?

• 1

• 2

• 3

• 4

Which element is only in set B?

• 6

• 7

• 5

• 8

Which elements are only in set C?

• 3, 11

• 3, 12

• 2, 11

• 2, 12

Which numbers are in the universal set but not in sets A, B, or C?

• 3, 5, 16-20

• 2, 5, 16-20

• 2, 4, 16-20

• 1, 2, 3

What is the cardinality of the set A intersect C, intersect B complement?

• 3

• 2

• 4

• 1