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Sets and Subsets: the Basics

Some "special" sets

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

Subsets

Given two sets and , we say that is a subset of if every element of is also an element of , and we write this as . is a proper subset of if it is not the empty set, and there exists at least one element of that is not in : we write this as .

Now it's your turn...

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