Question

The set of all natural numbers x for which x + 6 is less than 10. Use roster method​

Answer 1

1. $\underline \bold{\huge {ANSWER\::}}$

What is roster form?

● It is a form in which the elements of a set are written within curly brackets separated by a comma.

Example:

• A is a set containing the whole numbers less than 9.

○ Solution:-

A={0,1,2,3,4,5,6,7,8,9}

■Question 's solution:-

{1,2,3}

● Steps for solving:-

Given that ,

the set is of natural numbers i,e. like {1,2,3,...}.

Natural numbers begin from 1 and continue to the infinity.

2. But here , there is a condition.

3. The condition states that

the sum of the nos. and 6 should be less than 10 .

4. Now, we will solve this inequation:

$x + 6 < 10$

Transposing 6 to the right hand side, it becomes negative:

5. We have:

$x < 10 - 6 \\  \\ x < 4$

Thus, the elements of the set are natural nos. and less than 4.

6. Thus, ultimately we get the solution as:-

{1,2,3}.