Understanding Power Sets and Cardinality

The video tutorial explains how to find the power set of a given set A and determine its cardinality. It begins by defining the power set as the set of all subsets of A, including the empty set. The tutorial then demonstrates forming the power set by listing subsets with different numbers of elements. It clarifies that elements of the power set are sets, not individual numbers. Finally, it calculates the cardinality of the power set, which is the total number of subsets, and concludes with a count of eight subsets.

What is the power set of a set?

• A set containing only the largest subset

• A set containing only the empty set

• A set containing all possible subsets of the original set

• A set containing only the elements of the original set

Which of the following is always a subset of any set?

• The set itself

• The empty set

• A set with one element

• A set with two elements

How many single-element subsets can be formed from a set with three elements?

• One

• Two

• Three

• Four

What is the subset that contains all elements of the original set called?

• Empty subset

• Two-element subset

• Single-element subset

• Complete subset

Which of the following is NOT an element of the power set?

• A subset of the original set

• A number from the original set

• The complete set

• The empty set

Why can't a number from the original set be an element of the power set?

• Because the power set is empty

• Because numbers are not allowed in sets

• Because the power set only contains sets

• Because the power set only contains numbers

What is the cardinality of a power set of a set with three elements?

• Nine

• Three

• Six

• Eight

How is the cardinality of a power set determined?

• By multiplying the number of elements in the original set by two

• By counting the number of elements in the original set

• By counting the number of subsets in the power set

• By adding the number of elements in the original set

If a set has n elements, how many subsets does its power set contain?

• 2^n

• n^2

• n+1

• n

What is the significance of the empty set in the context of power sets?

• It is not part of the power set

• It is always included as a subset

• It is the same as the original set

• It is the largest subset