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.