Question

Write the following set in the set builder form \left\\{ {1,4,7,10,....} \right\\}

Answer 1

For writing a set in a set builder form all the elements of the set must be of the same form and from our given set we can see that the elements of the set is of the form $3x + 1$where x takes the value from 0.

Complete step-by-step answer:
In the set builder form, all the elements of the set must possess a single property to become the member of that set.
Here in our given set \left\\{ {1,4,7,10,....} \right\\}every element is of the form $3x + 1$, where $x \in W$
We can see that if x = 0
$\Rightarrow 3(0) + 1 = 1$
Which is the first element of the set
And if x=1
$\Rightarrow 3(1) + 1 = 3 + 1 = 4$
So all the elements can be given by .$3x + 1$., where $x \in W$
The given set can be written as \left\\{ {x|3x + 3,x \in W} \right\\}
Here ‘|’ denotes ‘such that’
Therefore the set builder form of the given set is .\left\\{ {x|3x + 3,x \in W} \right\\}.

Note: A set can be written in two other forms than set builder form. They are descriptive form and roster form.
In descriptive form the elements of the set are describes in words.And in roster form the elements in given in a tabular form