Introduction to Set Theory

2.1 Set Theory Basics: Symbols and Terminology

Vocabulary

A set is a collection of objects.

The objects belonging to a set are called elements or members.

Vocabulary

A set with no elements is called an empty set.

An empty set is also known as a null set.

An empty set can be denoted in the following ways: { } or ∅

You cannot show an empty set as {∅}.
*This shows a set containing one element (an empty set.)

Writing a Set

Methods of writing a set

Sets are designated using the 3 methods below.

• Word Description

• List

• Set builder

Writing a Set

The set of even counting numbers less than 10. (Word description)
{2, 4, 6, 8} (Listing Method)
{x| x is an even number less than 10} (Set-builder notation)

Match

Match the following terms or symbols with their definition.

• Set

• Empty Set

• Elements

• { } or ∅

A collection of objects.

A set containing no elements.

The objects belonging to a set.

Empty Set

• A collection of objects.

• A set containing no elements.

• The objects belonging to a set.

• Empty Set

Match

Match the following set notations to the correct method.

• The set of counting numbers between 6 and 13.

• {7, 8, 9, 10, 11, 12}

• {x | x is a counting number between 6 and 13}

Word Description

List

Set Builder

• Word Description

• List

• Set Builder

Match

Match the following

• The set of all even integers.

• {x | x is an even integer greater than 4 and less than 6}

• The set of five least positive integer powers of 2.

• The set of odd positive integers less than 10.

• The set of all negative integers

{..., -6, -4, -2, 0, 2, 4, 6,...}

∅

{2, 4, 8, 16, 32,}

{1, 3, 5, 7, 9}

{..., -4, -3, -2, -1}

• {..., -6, -4, -2, 0, 2, 4, 6,...}

• ∅

• {2, 4, 8, 16, 32,}

• {1, 3, 5, 7, 9}

• {..., -4, -3, -2, -1}

Match

Match set-builder notation to the correct list.

• {x | x is a month starting with the letter J}

• {x | x is a season of the year}

• {x | x is a month of the year}

• {x | x is a negative integer}

• {x | x is an odd integer between -4 and 10}

{January, June, July}

{spring, summer, fall, winter}

{January, February, March, ... December}

{-1, -2, -3, -4, -5, ...}

{-3, -1, 1, 3, 5, 7, 9}

• {January, June, July}

• {spring, summer, fall, winter}

• {January, February, March, ... December}

• {-1, -2, -3, -4, -5, ...}

• {-3, -1, 1, 3, 5, 7, 9}

Multiple Choice

Which description below results in an empty set?

• {x | x is an even integer between 6 and 10}

• {x | x is an even integer between 4 and 10}

• {x | x is an odd integer between 7 and 9}

• {x | x is an odd integer between 5 and 9}

Multiple Choice

Which description best describes the set shown?

{3, 5, 7, 9, 11}

• The set of counting numbers between 3 and 11.

• The set of counting numbers between 2 and 12.

• The set of odd counting numbers between 2 and 12.

• The set of even counting numbers between 2 and 12.

Multiple Choice

Which set best represents the set-builder notation given below?

{x | x is a counting number between 6 and 7}

• {6}

• {7}

• {6, 7}

• { }

Multiple Select

Which symbol or symbols are used to show an empty set?

• { }

• ∅

• {∅}

• None of the above