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Set Notation

Set notation is a way of describing the membership of and relationships between groups of objects, called elements. The language also dictates that you have to have what is called the universal set which denotes ALL items under consideration. This is usually denoted by the symbol U.

There are different ways of describing sets. Among them are using set notation and by means of Venn diagrams. We will be discussing set notation here first and then move on to Venn diagrams.

Set Notation

To demonstrate how set notations are used, we will take a look at a set of whole numbers between 1 and 10 in which case 10. To describe this set using set notation we could do the following:

 A = {  1,2,3,4,5,6,7,8,9,10 }

Now, to indicate that some thing is an element of a set you would use the following notation:

 2 ∈ A

This means that 2 is an element of set A.

Alternatively, you could also indicate the membership of a set by using rules. This is a common practice among technical people:

 { x is a natural number, x ≤ 10 }

This translates to:
x is a natural number such that x is less than or equal to 10. This can also be written as:

 {  x | x ∈  N, x ≤ 10 }

which in layman terms is expressed as:

 {  1,2,3,4,5,6,7,8,9,10 }

Now before we go into detail, there are set notations that are frequently used to denote a set of numbers that you should know about:

N - is a set of Natural or counting numbers such as 1,2,3,…

Z - is a set of integers, which include negative and positive integers.

Q - is a set of fractions such as ½  for half.

R - is a set of real numbers, which include integers, fractions and 
 irrational numbers or decimal numbers. in other words this are decimal numbers with 
infinite number of digits after the decimal point.

∅ or NULL set - denotes an empty set.

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Functions Notation

Venn Diagrams and set notation
A Venn diagram is a graphical notation used to show membership of and relationships among set elements. Let us say for example that our universal set has numbers 1,2,3 and 4 such that: Set A = {1,2} Set B = {2,3} Using ven diagrams, we can sho

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Set Notation

Set Notation

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