Lesson 3.5 - Working With Sets

Front

What is roster form in set theory?

Back

Roster form is a way of representing a set by listing all its elements within curly braces. For example, the set of natural numbers less than 5 can be written as {1, 2, 3, 4}.

Front

What is set-builder notation?

Back

Set-builder notation is a shorthand used to describe a set by stating the properties that its members must satisfy. For example, {x | x is a natural number and x < 5} describes the same set as {1, 2, 3, 4}.

Front

How do you write the set of even natural numbers less than 10 in roster form?

Back

The set of even natural numbers less than 10 in roster form is {2, 4, 6, 8}.

Front

What is the empty set?

Back

The empty set, denoted by ∅, is a set that contains no elements.

Front

How many subsets does a set with n elements have?

Back

A set with n elements has 2^n subsets.

Front

What is a subset?

Back

A subset is a set that contains some or all elements of another set. For example, if A = {1, 2, 3}, then {1, 2} and {1} are subsets of A.

Front

What is the universal set?

Back

The universal set is the set that contains all possible elements for a particular discussion or problem. It is usually denoted by the symbol U.

Front

What is the difference between a proper subset and a subset?

Back

A proper subset is a subset that contains at least one element from the original set but not all elements. For example, if A = {1, 2}, then {1} is a proper subset of A, but {1, 2} is not.

Front

How do you represent the set of all integers in set-builder notation?

Back

The set of all integers can be represented in set-builder notation as {x | x is an integer}.

Front

What is the intersection of two sets?

Back

The intersection of two sets A and B, denoted by A ∩ B, is the set of elements that are common to both A and B.