A (**data**) **set** is a collection of (**data**)** elements**. We can explicitly list the elements in the set or define the set by a property

The set *A* consists of the 6 listed elements. The set *B* consists of apples, pears, bananas, etc.

A data element *a* **belongs** to a set *A*, written *a ** A*, provided *a* is a **member** of the set *A*. E.g. in the examples above, 3 * A*, but 4 doesn’t belong to *A* (written 4 *A*).

The following are common operations on sets:

We also use the symbol Ø to represent the **null set**, i.e. the set containing no elements.

Sets obey a number of laws including the following (where *S* = the universal set containing everything under study):

An **interval** is the collection of values between two numbers. If *a < b* then we can define the following types of intervals:

The **integers** are a set consisting of the whole numbers = {…-3,-2 , -1, 0, 1, 2, 3, …}

Dear Charles

I dont understand how these two are correct.(a,b)={x:a<x<b}

and [a,b]={x:a<_x<_b}

i think only one should be correct.

kindly help me.

If by <_ you mean "less than or equal", then both are correct. This is because "less than" is different from "less than or equal". Charles

Hi Charles,

I was confused by the statement above that A = (A∩B) ∪ (A∪B′).

It seemed to me that it should be A = (A∩B) ∪ (A∩B′).

Then on the Basic Probability Concepts page I note you do state it as I thought it should be, so I believe it should be changed above.

Steve,

Yes, you are correct. Thank you very much for catching this typo. I have now corrected the formula on the referenced webpage.

I appreciate your help in improving the website.

Charles

Hi Charles,

Thank you for all this information. I’m wondering…..what does the ‘ mean in A U A’ = S??

It’s been a long time and it’s not ringing a bell. Thanks.

Hi Jonathan,

A’ = the complement of A = the set of elements in the sample space S that are not in S. If S = {1,2,3,4,5} and A = {2,4} then A’ = {1,3,5}

Charles

Hello Charles,

Congratulations with your site.

A minor typo:

A∪(B∩C)=(A∪B)∩(A∪B)

should be

A∪(B∩C)=(A∪B)∩(A∪C)

In the same way:

A∩(B∪C)=⋯

Best regards

Jan

Hello Jan,

Thank you very much for catching this typo. I have just changed the referenced webpage to make the necessary correction.

I really appreciate your effort to make the website better.

Charles