Question

Describe the following sets in set-builder form:
C = {0, 3, 6, 9, 12…}

Answer 1

Hint: In set builder form, the set is represented by writing a rule inside a pair of brackets, in such a way that the set is well defined. All the elements of the set must have a single property in the set builder form to become the component of that set. For example: Let A be the set of all the multiples of 2. So, in Set Builder form it can be represented as: A = {a: a = 2$\times$c, where c$\in$W}. Use this hint to describe the set C in set- builder form.

Complete step-by-step answer:
We have been given that C = {0, 3, 6, 9, 12,...}.
As we can see that every element in set C can be represented in the form 3$\times$a where a is a whole number.
So, in set builder form Set C can be represented as C={c: c=3$\times$a, where c$\in$W}.
In above set builder form the capital letter ‘W’ represents the set of whole numbers.

Note: Apart from set builder form a set can be represented in two other forms these are:

1. Statement Form: In this form a well-defined description of the elements of the set is given and is then enclosed in curly brackets.
   Example: C={c is equal to 3$\times$a where a is a whole number}
2. Roster Form: In this method elements of the set are listed within the pair of brackets { } and are separated by commas the form in which set C is represented in question is the tabular or roster form.