Question

Write the following set in roster form: A = {x: x is an integer and -3 < x < 7}

Answer 1

Hint: Roster form can be given for set A by writing the values of elements belonging to it within {} and are separated by commas. The given set A is of the set-builder form where we use statements within the bracket i.e., {}.

Complete step by step solution:
Here, we need to know the terms for representing any set in two ways, one is roster form and other is set builder form.
Now, we know that we represent any set in form of words in set builder form and in terms of elements in roster form.
So, we have set ”A” as
A = {x: x is an integer and -3 < x < 7}
Now, we need to write the exact values of ‘x’ possible for the given set ‘A’ in roster form.
We can observe that there will be only nine elements between the values -3 and 7 as per the statement -3 < x <7.
Here we need not to include -3 and 7, as -3 and 7 are not included in the expression -3 < x < 7. Hence there will be nine elements in the set A and which can be given as $\left\{ -2,-1,0,1,2,3,4,5,6 \right\}$ in the roster form of the set A
Hence, roster form of the given set can be represented as
$A=\left\{ -2,-1,0,1,2,3,4,5,6 \right\}$

Note: One may include -3 and 7 as well with the elements of A which is wrong as -3 and 7 are not included in the expression -3 < x < 7.
One should be very clear with the terms roaster form and set builder form to solve these kinds of problems.