# Sets and Subsets: the Basics

- Author:
- Simona Riva

- Topic:
- Set Theory

## What is a Set?

A is used to say that an .
The symbol is used to say that an .
We can also represent sets

**set**is an*unordered collection of objects*, usually called*elements*or*members*of the set. We can**represent a set**by*listing*its elements, or by defining the*property*of all the elements in the set (set-builder notation)*Example*:*A*={60, 62, 64, 66, 68, 70} and*A*={*x*| 60 ≤*x*< 71,*x*is an even integer} are two representations of the same set. This symbol**element belongs to a set**, for example**element does not belong to a set**, for example**geometrically**, using Venn diagrams: closed lines enclose portions of the plane that represent the sets, whose elements are represented with points inside the closed lines.## Some "special" sets

The , 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.

**empty set**is denoted with the symbol ∅, and is a set that has no elements. The**universal set**is in general denoted as## Subsets

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

**subset**of**proper subset**of## 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.

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