[br]This lesson serves as an introduction to the concept of sets as used in a general context. In this lesson, you'll be introduced to basic [color=#0000ff]Set Vocabulary[/color] and the two common methods of naming sets—the [color=#0000ff]Roster[/color] or [color=#0000ff]List Method[/color] and the [color=#0000ff]Rule[/color] [color=#0000ff]Method[/color] or [color=#0000ff]Set-Builder Notation[/color]. In succeeding lessons, you'll expand your set vocabulary and learn more about sets—types of sets, subsets, and operation on sets.[br][br][color=#0000ff]BASIC SET VOCABULARY[/color][br][color=#0000ff][br]Set[/color]—any [color=#6aa84f]well-defined[/color] collection of objects.[br][br] Examples: T = set of tableware in the picture above (a well-defined group)[br] V = set of vowels in the English alphabet (a well-defined group)[br] E = set of even numbers (a well-defined group)[br][br] Non-example: N = group of fast swimmers in the Olympics ([color=#ff0000]NOT[/color] a well-defined group)[br][br][color=#0000ff]Element[/color] or [color=#0000ff]member[/color]—objects in a set[br][br] [color=#6aa84f]∈[/color] — "is an element of"[br][br] [color=#ff0000]∉[/color] — "is not an element of"[br][br] Examples: plate [color=#6aa84f]∈[/color] T, a [color=#6aa84f]∈[/color] V[br] baseball [color=#ff0000]∉[/color] T, b [color=#ff0000]∉[/color] V[br][br][color=#0000ff]METHODS OF NAMING SETS[/color][br][br]Capital letters of the English alphabet are normally used to name sets. [br][br][color=#0000ff]Roster[/color] or [color=#0000ff]List Method—[/color]list or enumerate all the elements, without repetition, separated by commas, and enclosed within [color=#0000ff]{ }[/color] braces[br][br] Example: V = {a, e, i, o, u}[br] E = {2, 4, 6, 8} [br][br][color=#0000ff]Rule[/color] [color=#0000ff]Method[/color] or [color=#0000ff]Set-Builder Notation[/color]—state the defining characteristics of the set or write an algebraic expression to generate the members of the set, also enclosed within braces[br][br] Example: V = {vowels in the English alphabet}[br] E = {positive even numbers less than 10} or {positive even numbers less than or equal to 8}[br] or {2x | x is a positive integer less than 5} or {2x | x is a positive integer less than or[br] equal to 4}

[br]Below is a set of problems that require you to name sets using the two common methods of naming sets.

In future lessons, you'll learn additional set vocabulary and other information involving sets. Did you ENJOY today's lesson?