Question

Write the set D = {-6, -4, -2, 0, 2, 4, 6} in the set – builder form.

Answer 1

Hint: Set – builder form is a notation for the elements of the set which describes the property that each member of the set holds. In the above set, the general term for the elements of the set is 2n where n is an integer and belongs from -3 to +3.

Complete step-by-step answer:
The set given in the question is:
D = {-6, -4, -2, 0, 2, 4, 6}
The elements in the above set are divisible by 2. The first term of the set is 2(-3), the second term of the set is 2(-2), the third term of the series is 2(-1) and the last term of the set is 2(3).
So, the general term for the elements of the set is 2n where n is an integer and takes value from -3 to +3.
The set – builder form of the set D = {-6, -4, -2, 0, 2, 4, 6} is:
{x: 2n where $n\in Z$and -3≤n≤3}
In the above set – builder form, “Z” represents integers and the inequality -3≤n≤3 shows that n takes value from -3 to 3.
The format to write a set – builder form of any set is that first we should write a variable “x” then put a colon “:” then write the general term like 2n then describe what is n in 2n and write the whole set – builder form in the curly brackets.
Hence, the set – builder form for the given set is {x: 2n where $n\in Z$and -3≤n≤3}.

Note: If in the question we have asked to write a set of the elements from the set – builder form how are we going to write it.
The set – builder form of the given set is:
{x: 2n where $n\in Z$and -3≤n≤3}
Substituting n = -3 in 2n then the first element is -6.
Substituting n = -2 in 2n then the second element is -4.
Substituting n = -1 in 2n then the third element is -2.
Likewise, we will find the elements of the set till n = 3.