Question

What is roster or set builder form?

Answer 1

Roster form or tabular form:

In this, elements of the set are listed within the pair of brackets { } and are separated by commas. 

For example:

(i) Let N denote the set of first five natural numbers.
Therefore, N = {1, 2, 3, 4, 5}        → Roster Form

(ii) The set of all vowels of the English alphabet. 
Therefore, V = {a, e, i, o, u}        → Roster Form

(iii) The set of all odd numbers less than 9. 
Therefore, X = {1, 3, 5, 7}        → Roster Form

(iv)  The set of all natural number which divide 12. 
Therefore, Y = {1, 2, 3, 4, 6, 12}        → Roster Form

(v) The set of all letters in the word MATHEMATICS.
Therefore, Z = {M, A, T, H, E, I, C, S}        → Roster Form

(vi) W is the set of last four months of the year.
Therefore, W = {September, October, November, December}        → Roster Form

Note:

The order in which elements are listed is immaterial but elements must not be repeated. 

Set builder form:

In this, a rule, or the formula or the statement is written within the pair of brackets so that the set is well defined. In the set builder form, all the elements of the set, must possess a single property to become the member of that set. 

In this form of representation of a set, the element of the set is described by using a symbol ‘x’ or any other variable followed by a colon The symbol ‘:‘ or ‘|‘ is used to denote such that and then we write the property possessed by the elements of the set and enclose the whole description in braces. In this, the colon stands for ‘such that’ and braces stand for ‘set of all’.