These lessons are part of a series of lessons on

sets.

In these lessons, we will learn
the concept of a set, methods for defining sets, set notations, empty set, symbols for ‘is an element of’, subset, intersection and union.

Related Topics:

More Lessons on Sets
## Sets

A

set is a well-defined collection of distinct objects.

The individual objects in a set are called the

**members** or

**elements** of the set.

Some notations for sets are:

A = {1, 2, 3} = {integers greater than 0 and less than 4}
= {x: x is an integer and 0 < x < 4}

We also have the empty set denoted by {} or Ø.

We can have infinite sets for example {1, 2, 3, ...}

We have a symbol showing membership.We relate a member and a set using the symbol ∈. If an object

*x* is an element of set

*A*,
we write

* x* ∈

*A*. If an object

*z* is not an element of set

*A*, we write

*z* ∉

*A*.

∈ denotes “is an element of’ or “is a member of” or “belongs to”

∉ denotes “is not an element of” or “is not a member of” or “does not belong to”

*Example*:

If *A* = {1, 3, 5} then 1 ∈ *A * and 2 ∉ *A*

## Videos

This video introduces the concept of a set and various methods for defining sets.

Set Notation(s)

A discussion of set notation: lists, descriptions, and set-builder notation.

The following video describes: Set Notations, Empty Set, Symbols for ҩs an element ofҬ subset, intersection and union.

Set Notation

Roster Method, Set Builder Notation.

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