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 = the  set  of  all  integers={…,−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:

Z={x:x  is  an  integer}

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

M={x | x>3}

(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 x∈A, and if x is not an element of A we write x∉A.

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