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You can skip to the next lesson if you already understand set builder


There are two methods of representing a set :

(i) Roster or tabular form

(ii) Set-builder form.

Roster or tabular form: In roster form, all the elements of a set are listed, the elements are being separated by commas and are enclosed within braces { }.

For Example:

Z = thesetofallintegers={,3,2,1,0,1,2,3,}

Set-builder form: In the set builder form, all the elements of the set, must possess a single property to become the member of that set.

For Example:


You can read Z={x:xisaninteger}  as “The set Z equals all the values of x such that x is an integer.”


(This last notation means “all real numbers x such that x is greater than 3. So, for example, 3.1 is in the set M, but 2 is not. The vertical bar | means “such that”.)

You can also have a set which has no elements at all. This special set is called the empty set, and we write it with the special symbol ∅.

If x is a element of a set A, we write xA, and if x is not an element of A we write xA.

So, using the sets defined above,

862 Z, since 862 is an integer, and

2.9 M, since 2.9 is not greater than 3

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