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The Empty Set and Set Equality

This lesson is part of a series of lessons on sets.

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

How to define sets and elements>
A set is composed of elements or members. A set is denoted by capital letters.
A = {a, b, c, d}, a ∈ A, a belongs to A
B = {e, f, g, h}, a ∉ B
A set can be defined in the following ways:
1. Listing all the elements, A = {a, b, c, d}
2. Describing the properties held by the members
A = {first 4 letters of the alphabet}

This video introduces the concept of a set and various methods for defining sets. The Null set or Empty set

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:

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.

What is the Null Set or Empty Set?

Set Equality

What are equal sets?

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.

Learn about equal sets
How 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.


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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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