Question

Write the following set in set builder form: {2, 3, 5, 7, 11, 13, 17, 19, 23, …..}.

Answer 1

Hint: In set builder form, the properties of the elements in the set is assigned to a variable, all of which is contained inside the braces. So, determine the property of the elements of the set and express it in set builder form.

Complete step by step answer:
A set is a collection of well-defined objects. It can be represented in two forms:

(i). Roster form

(ii). Set-Builder form

In the given question, we need to express the set in set-builder form, where there is a variable representing any element of the set followed by a property satisfied by every member of the set.

The given set is already expressed in roster form, where the elements of the set are listed within braces and are separated by commas. The elements appear only once and the order does not matter.

So, we need to determine the properties of the elements of the set given in roster form.
We know that 2, 3, 5, 7, 11, 13, 17, 19, 23 and so on are prime numbers. Hence, the set contains elements which are prime numbers.

Hence, we can represent the given set in set-builder form as follows:

{x: x is a prime number}

Hence, the answer is {x: x is a prime number}.


Note: Do not try to find any arithmetic relations between the elements, first, observe all the elements and make a conclusion.