[b]Definition: [/b]For the purposes of this applet, any [b]well defined [/b]collection of objects having common characteristics is going to be regarded as a [b]set.[/b] Each object is known as [b]member[/b] or [b]element [/b]of the set.[br][br][b]Notation: [/b]Sets are usually denoted by capital letters [math]A,B,C,\ldots[/math], while their elements are denoted by lower case letters [math]a,b,c,\ldots[/math]. If [math]a[/math] is an element of a set [math]A[/math], then it is denoted as [math]a\in A[/math].[br][br][b]Definition: [/b]A set with no members is called [b]empty set [/b]and it is denoted as [math]\varnothing[/math] or [math]\left\{\right\}[/math].[br][br][b]Definition:[/b] Two sets [math]A[/math] and [math]B[/math] are said to be [b]equals [/b]if every member of [math]A[/math] belongs to [math]B[/math] and every member of [math]B[/math] belongs to [math]A[/math].

The set is described by [b]listing the properties that describe the elements of the set[/b]. Set-builder notation is comprised by two parts; namely:[br][list][*]A variable [math]x,y,z,a,b,c,\ldots[/math], representing any elements of the set.[/*][*]A property which defines the elements of the set.[/*][/list][b][br]Notation:[/b] If [math]x[/math] is the variable and [math]p(x)[/math] is the property that object [math]x[/math] must comply to be a member of the set, then it is usually denoted as: [math]\left\{x|p\left(x\right)\right\}[/math].[br]

In this method [b]all of the member [/b]of the set are displayed, separated by commas.

[b]Definition: [/b]Let [math]A[/math] and [math]B[/math] be two sets. The [b]union [/b]of [math]A[/math] and [math]B[/math] is the set whose members are elements of [math]A[/math] [b]or[/b] [math]B[/math].[br][br][b]Notation: [/b]The union of sets [math]A[/math] and [math]B[/math] is denoted as [math]A\bigcup B[/math]; that is:[br][br][center][math]A\bigcup B=\left\{x|x\in A\vee x\in B\right\}[/math],[br][br][/center]where symbol [math]\vee[/math] represents [b]or[/b].

[b]Definition: [/b]Let [math]A[/math] and [math]B[/math] be two sets. The [b]intersection [/b]of [math]A[/math] and [math]B[/math] is the set whose members are elements of [math]A[/math] [b]and[/b] [math]B[/math].[br][br][b]Notation: [/b]The intersection of sets [math]A[/math] and [math]B[/math] is denoted as [math]A\bigcap B[/math]; that is:[br][br][center][math]A\bigcap B=\left\{x|x\in A\wedge x\in B\right\}[/math],[br][br][/center]where symbol [math]\wedge[/math] represents [b]and[/b].

[b]Definition: [/b]Let [math]A[/math] and [math]B[/math] be two sets. The [b]difference [/b]of [math]A[/math] and [math]B[/math] is the set whose members are elements of [math]A[/math] [b]but they do not belong to[/b] [math]B[/math].[br][br][b]Notation: [/b]The difference of sets [math]A[/math] and [math]B[/math] is denoted as [math]A\backslash B[/math]; that is:[br][br][center][math]A\backslash B=\left\{x|x\in A\wedge x\notin B\right\}[/math].[/center]

Use the following applet to practice finding the union, the intersection and the difference of the given sets.