Question

Describe the following set in set – builder form:
{2, 4, 6, 8……….}

Answer 1

Hint: Set – builder form is a general notation to write the elements of the set which describes the properties of the members of the set. In the set given above, the general term is 2n where n belongs to a natural number. So, using this general term we can write the set – builder form.

Complete step-by-step answer:
The elements given in the above set is as follows:
{2, 4, 6, 8……….}
The elements given in the above set are divisible by 2. And the first term is 2 multiplied by 1. The second term is 2 multiplied by 2. The third term is 2 multiplied by 3. So, we can say that the general term of the elements given in the set is 2n where n belongs to the natural number starting from 1.
The set – builder form of the given set {2, 4, 6, 8……….} is:
{x: 2n where $n\in N$ and n = 1, 2, 3……..}
In the above set – builder form, “N” represents the natural numbers.
The format to write a set – builder form of any set is that first we should write a variable “x” then put a colon “:” then write the general term like 2n then describe what is n in 2n and write the whole set – builder form in the curly brackets.
Hence, the set – builder form of the given set is {x: 2n where $n\in N $and n = 1, 2, 3……..}.

Note: We can also write the set – builder of the given set as {x: x is an even natural number}.
We know that 1, 2, 3, 4………..are natural numbers.
Then 2, 4, 6, 8, 10…… are even natural numbers.
So, the set builder of the given set is {x: x is an even natural number}.