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
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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 
The following are common operations on sets:
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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):
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An interval is the collection of values between two numbers. If a < b then we can define the following types of intervals:
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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