Understanding Subsets and Cardinality

The video tutorial explains how to find a subset with the greatest cardinality that is common to two sets, A and B. It begins by defining a subset and then describes how to find the intersection of sets A and B, which is the set with the largest cardinality that is a subset of both. The tutorial analyzes the elements in sets A and B, identifying the intersection as the set containing elements 8, 9, 10, 11, 12, and 15. The cardinality of this intersection is six, making it the largest subset common to both sets.

What is the main objective of the problem discussed in the video?

• To calculate the sum of elements in sets A and B

• To determine the difference between sets A and B

• To find a subset with the greatest cardinality that is a subset of both A and B

• To find the union of sets A and B

What does it mean for set C to be a subset of set A?

• Every element of C is also an element of A

• Set C is identical to set A

• Set C and set A have no elements in common

• Set C has more elements than set A

What is the significance of the intersection of sets A and B?

• It contains elements that are only in set A

• It contains all elements that are in both sets A and B

• It contains elements that are only in set B

• It contains no elements

Which elements are found in the intersection of sets A and B?

• 1, 2, 3, 4, 5

• 13, 14, 15, 16, 17

• 8, 9, 10, 11, 12, 15

• 6, 7, 8, 9, 10

Why is the intersection of sets A and B considered to have the greatest cardinality?

• It is the smallest possible subset of both A and B

• It is the largest possible subset of both A and B

• It contains elements not present in either A or B

• It has the fewest elements

What is the cardinality of set C?

• Four

• Five

• Six

• Seven

What is the relationship between set C and sets A and B?

• Set C is a subset of both sets A and B

• Set C is a superset of sets A and B

• Set C is a union of sets A and B

• Set C is disjoint from sets A and B

If a set has fewer elements than set C, what can be said about it?

• It is identical to set C

• It is a superset of set C

• It is a subset of sets A and B but with less cardinality

• It is not a subset of sets A and B

What is the purpose of listing the elements of set C?

• To show the elements that are not in sets A and B

• To demonstrate the elements that are in the union of sets A and B

• To identify the elements that form the intersection of sets A and B

• To list elements that are exclusive to set C

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

• Six

• Five

• Seven

• Four