Question

Write the set of even natural numbers in roster form.

Answer 1

Hint:Elements in roster form are separated by commas and are enclosed by {} brackets.

In this question first we find all the even natural numbers and then represent those even natural numbers in the roster form.

Natural numbers are all the whole numbers excluding the number 0. All natural numbers can be whole numbers but all whole numbers are not natural numbers.

Natural numbers can be \[N = \left\{ {1,2,3,4,5,6,7,8,9.......} \right\}\]

Complete step by step solution:
Let the set of even natural number be ‘E’

Now we know the numbers which are divisible by 2 are known as even numbers.
Hence the natural even numbers can be\[2,4,6,8,.......\], here if we divide each of the number by 2 then we can see all the numbers get divided by 2 but if they are not divisible by 2 then they are not even number.

Now we know in roster form all the element of the set are separated by commas and are enclosed by {}
brackets, hence we can write those even numbers in the roster form as
\[E = \left\{ {2,4,6,8,.......} \right\}\]

Therefore the set of even natural numbers in roster form is \[E = \left\{ {2,4,6,8,.......} \right\}\]

Note: There are three main types of set and they are written as:

1) Statement form
In Statement form we write: Set of all natural number, which are divisible by 2

2) Roster or tabular form
In roster form:\[\left\{ {2,4,6,8,.......} \right\}\]

3) Rule or set builder form
In set builder form: {x: x is a natural number, which are divisible by 2}