Understanding Set Cardinality and Multiples

The video tutorial explains how to determine the number of elements in a set of integers from 1 to 2218 that are multiples of 3, 5, or 8. It introduces sets A, B, and C for multiples of 3, 5, and 8 respectively, and discusses their intersections. The cardinality of each set and intersection is calculated using division and rounding down. The formula for the union of sets is applied to find the total number of multiples, resulting in 1,183 elements. The tutorial provides a step-by-step approach to solving the problem using set theory and arithmetic.

What is the range of integers considered in the problem?

• 1 to 1000

• 1 to 2218

• 1 to 5000

• 1 to 3000

Which set contains multiples of 5?

• Set A

• Set B

• Set C

• Set D

What is the intersection of sets A and B?

• Multiples of 8

• Multiples of 24

• Multiples of 40

• Multiples of 15

What is the term used to describe the number of elements in a set?

• Union

• Intersection

• Cardinality

• Subset

How is the cardinality of a set determined in this problem?

• By dividing the range by the multiple and rounding down

• By dividing the range by the multiple and rounding up

• By multiplying all elements

• By adding all elements

What is the cardinality of set A?

• 739

• 443

• 277

• 147

What is the cardinality of the intersection of sets A and C?

• 92

• 147

• 55

• 18

What is the cardinality of the intersection of sets B and C?

• 92

• 55

• 18

• 147

What is the final result of the cardinality of the union of sets A, B, and C?

• 277

• 443

• 739

• 1183

How many elements in the set are multiples of 3, 5, or 8?

• 277

• 739

• 443

• 1183