A [b]set [/b]is an [i]unordered collection of objects[/i], usually called [i]elements [/i]or [i]members [/i]of the set.[br][br]We can [b]represent a set[/b] by [i]listing [/i]its elements, or by defining the [i]property [/i]of all the elements in the set (set-builder notation)[br][br][i]Example[/i]:[br][i]A[/i]={60, 62, 64, 66, 68, 70} and [br][i]A[/i]={[i]x[/i] | 60 ≤ [i]x [/i]< 71, [i]x[/i] is an even integer} [br]are two representations of the same set.[br][br]This symbol [math]\in[/math] is used to say that an [b]element belongs to a set[/b], for example [math]a\in A[/math]. [br]The symbol [math]\notin[/math] is used to say that an [b]element does not belong to a set[/b], for example [math]b\notin A[/math].[br][br]We can also represent sets [b]geometrically[/b], using [url=https://en.wikipedia.org/wiki/Venn_diagram]Venn diagrams[/url]: closed lines enclose portions of the plane that represent the sets, whose elements are represented with points inside the closed lines. [br][br]

The [b]empty set[/b] is denoted with the symbol ∅, and is a set that has no elements.[br][br]The [b]universal set[/b] is in general denoted as [math]U[/math], and contains all the possible elements from which it's possible to extract the elements of a set.[br]The Venn representation of the universal set is a rectangle.

Given two sets [math]A[/math] and [math]B[/math], we say that [math]B[/math] is a [b]subset [/b]of [math]A[/math] if every element of [math]B[/math] is also an element of [math]A[/math], and we write this as [math]B\subseteq A[/math].[br][br][math]B[/math] is a [b]proper subset[/b] of [math]A[/math] if it is not the empty set, and there exists at least one element of [math]A[/math] that is not in [math]B[/math]: we write this as [math]B\subset A[/math].

Try the activity below:[br]drag the sets and explore sets and subsets by viewing their representations with a Venn diagram.