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In this lesson, we will learn how to define sets, the empty set, equal sets, subset, superset, proper subset, and proper superset.

Related Topics: More Lessons on Sets

There are some sets that do not contain any element at all. For example, the set of months with 32 days. We call a set with no elements the null or empty set. It is represented by the symbol { } or Ø .

Some other example of null sets are:

This video introduces the concept of a set and various methods for defining sets.The set of dogs with six legs.

The set of squares with 5 sides.

The set of cars with 20 doors.

The set of integers which are both even and odd.

The Null Set or Empty Set

Consider the sets:

*P* ={Tom, Dick, Harry, John} * Q* = {Dick, Harry, John, Tom}

Since *P* and *Q *contain exactly the same number of members and the members are the same, we say that *P* is equal to *Q*, and we write *P* = *Q*. The order in which the members appear in the set is not important.

Consider the sets:

*R* = {2, 4, 6, 8} *S* = {2, 4, 6, 8, 10}

Since *R* and *S* do not contain exactly the same members, we say that *R* is not equal to *S* and we write *R ≠ *S*.*

Equal Sets Video

Learn about equal sets.

Sets can be related to each other in different ways.

This video describes the set relations of equality, subset, superset, proper subset, and proper superset.