# Describe the following sets in set-builder form:

$D = \left\{ {10,11,12,13,14,15} \right\}$

Answer

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Hint: You have to understand the form of sets. You should have knowledge of roster form and also set builder form. That means you have to write it in symbolic form.

Roaster form(Tabular form): All the elements of a set are listed, the elements are being separated by commas and are enclosed in braces.

Set builder form: You have to write it in symbolic form the common characteristics shared by all the elements of the set.

Complete step-by-step answer:

We have

$D = \left\{ {10,11,12,13,14,15} \right\}$

When we write it in set builder form

$D = \left\{ {x:x{\text{ is a natural number; 10}} \leqslant {\text{x}} \leqslant {\text{15}}} \right\}$

Note: Whenever you get this type of question the key concept of solving is you have to write it in set builder form that means you have to find a property which is common to all the elements of that set, and using that property you have to represent all the elements.

Roaster form(Tabular form): All the elements of a set are listed, the elements are being separated by commas and are enclosed in braces.

Set builder form: You have to write it in symbolic form the common characteristics shared by all the elements of the set.

Complete step-by-step answer:

We have

$D = \left\{ {10,11,12,13,14,15} \right\}$

When we write it in set builder form

$D = \left\{ {x:x{\text{ is a natural number; 10}} \leqslant {\text{x}} \leqslant {\text{15}}} \right\}$

Note: Whenever you get this type of question the key concept of solving is you have to write it in set builder form that means you have to find a property which is common to all the elements of that set, and using that property you have to represent all the elements.

Last updated date: 21st Sep 2023

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