Question

Write \[F{\text{ }} = {\text{ }}\left\{ {5,{\text{ }}10,{\text{ }}15,{\text{ }}20} \right\}\]in set builder form
A) \[F{\text{ }} = {\text{ }}\{ x|x{\text{ }} = {\text{ }}5n,{\text{ }}n \in N,{\text{ }}n{\text{ }} < {\text{ }}4\} \]
B) \[F{\text{ }} = {\text{ }}\{ x|x{\text{ }} = {\text{ }}5n,{\text{ }}n \in N,{\text{ }}n{\text{ }} \leqslant {\text{ }}4\} \]
C) Cannot be determined
D) None of these

Answer 1

Hint: To solve this question, i.e., to write the set in a set builder form. We will check first what kind of set we are given. After analysing the set, we will write in set builder form, by specifying the given elements of the set. So, here, the given set is a series of natural numbers upto \[20\] and the numbers are divisible by \[5.\] So, we will see the given options and check which satisfies the question, and hence we will get one answer out of four multiple choices.

Complete step-by-step answer:
We have been given a set, \[F{\text{ }} = {\text{ }}\left\{ {5,{\text{ }}10,{\text{ }}15,{\text{ }}20} \right\}\]. We need to write this set in a set builder form.
The set which are given to us here has natural numbers upto \[20\] and all the given numbers are divisible by \[5.\] So, we can write the set in set builder form as:
\[F{\text{ }} = {\text{ }}\{ x|x{\text{ }} = {\text{ }}5n,{\text{ }}n \in N,{\text{ }}n{\text{ }} \leqslant {\text{ }}4\} \]
Hence, option (B) \[F{\text{ }} = {\text{ }}\{ x|x{\text{ }} = {\text{ }}5n,{\text{ }}n \in N,{\text{ }}n{\text{ }} \leqslant {\text{ }}4\} \], is correct.

Note: In set builder form, we describe a set by specifying the elements, which its members only satisfy. We can also check that the set builder form which we have written for the given set is correct or incorrect, method is mentioned below.
Given set: \[F{\text{ }} = {\text{ }}\left\{ {5,{\text{ }}10,{\text{ }}15,{\text{ }}20} \right\}\]
Set builder form: \[F{\text{ }} = {\text{ }}\{ x|x{\text{ }} = {\text{ }}5n,{\text{ }}n \in N,{\text{ }}n{\text{ }} \leqslant {\text{ }}4\} \]
Here, if we see, $n \leqslant 4$, i.e., the number of terms are less than equals to four, which is correct.