Question

Write the roster form of the given set: $A =$ {$ x: \text{x is an integer}, -3 < x < 3$}.

Answer 1

Hint: Use the definition of roster form which says that in the roster from, we write all the possible elements of the given set within the brackets { } to write the given set in roster form.

Complete step by step answer:
We have to write the given set $A =$ {$ x: \text{x is an integer}, -3 < x < 3$} in the roster form.
We first observe that we are given the set in set builder form. In the set-builder form, a rule or a formula or a statement is written within the pair of brackets { } so that the set is well defined.
We will now write the given set in the roster form. We know that in set roster form, we write all the possible elements of the given set within the brackets { }.
We will include all the possible integers greater than -3 and less than 3 to write the set roster form of the given set $A =$ {$ x: \text{x is an integer}, -3 < x < 3$}.
So, we have $x=-2,-1,0,1,2$.
Thus, the set A in set roster form is $A=\left\{ -2,-1,0,1,2 \right\}$.
Hence, we can write the given set in set roster form as $A=\left\{ -2,-1,0,1,2 \right\}$.

Note: One must keep in mind that in the set-builder form, all the elements of the set must possess a single property to become a member of the set. We should remember that in set roster form, the order of elements of the set doesn’t matter, but the elements should not repeat within the set. We can also write a set in statement form. In this form, a well-defined description of elements of the set is given and it is enclosed within curly brackets { }.