Set Theory Concepts and Definitions

The video tutorial covers various types of sets, including empty, singleton, finite, and infinite sets. It explains equal and equivalent sets, universal sets, subsets, proper subsets, supersets, and proper supersets. The tutorial also discusses the concept of power sets and how to calculate the number of subsets using the formula 2^n, where n is the number of elements in the set.

What is the cardinality of an empty set?

• 1

• 0

• Depends on the set

• Infinite

Which of the following is a singleton set?

• {1, 2}

• {a}

• {}

• {1, 2, 3}

What makes two sets equal?

• Both are finite

• Both are infinite

• Same elements

• Same number of elements

What is a universal set?

• A set with infinite elements

• A set with no elements

• A set containing all elements

• A set with one element

How many subsets does a set with 3 elements have?

• 9

• 3

• 6

• 8

What is a proper subset?

• A set that is equal to another set

• A set that contains all elements of another set

• A set with no elements

• A set that is a subset but not equal to another set

What is a superset?

• A set that is equal to another set

• A set that contains all elements of another set

• A set with no elements

• A set with one element

Which of the following is a proper superset?

• A set equal to another set

• A set that contains all elements of another set but is not equal

• A set with no elements

• A set with fewer elements than another set

What is the power set of a set with 3 elements?

• A set with 3 elements

• A set with 6 elements

• A set with 8 elements

• A set with 9 elements

How is the number of elements in a power set calculated?

• 2^n

• n^2

• 2n

• n+2