Question

The set B=\left\\{ 1,2,3,6,9,18 \right\\} can be written in the set builder form as
A. B=\left\\{ \text{All factors of 18} \right\\}
B. $B$ is the set of all factors of $18$
C. B=\left\\{ X|X\text{ is a factor of 18} \right\\}
D. B=\left\\{ X|X\text{ is a multiple of 3} \right\\}

Answer 1

Before solving this question first we have to look at the definition of set builder form. Set builder is a notation used to write sets, usually used to write sets with an infinite number of elements. When we write the set builder form, we analyze each element of a set. Each element should satisfy the condition given.

Complete step by step answer:
We know that a set is a collection of different objects. We have two ways to represent the same - set builder form and roster form. In the roster form of set, we represent the elements directly, say, A = {1, 2, 3, 4}. In set builder form, we have the elements given as, say, A = {x|x is a natural number less than 5}. We can see that here the elements of sets are given as a condition and only those values of x which satisfy the condition are considered. So, here we have obtained the set builder form of a set given in the roster form.
Here we have given set B=\left\\{ 1,2,3,6,9,18 \right\\}
When we analyze the options given we see that the option A and option B are not the correct representation of set builder form. So, both the options are incorrect. Also, option D is incorrect because $2$ is not a multiple of $3$.
When we analyze the elements of set $B$, we realize that all the elements are factors of $18$.
According to the given options, option $C$ is the correct way to represent the set $B$.
The correct way to write a set builder form for the given set is B=\left\\{ X|X\text{ is a factor of 18} \right\\}

So, the correct answer is “Option C”.

Note: Here in this question students may confuse while choosing a correct option. Option B is also explaining the set $B$ but it is not the correct way to represent a set into set builder form. So, option B is incorrect. Most students get confused between factor and multiple. Just remember that multiple of a number is essentially obtained by multiplying that number n number of times. So it will be greater than that number. Factors of a number are numbers that are multiplied to that number so as to get multiples of that number. It will be equal to or less than that number.