Question

Write the set B = {1, 2, 4, 7, 14, 28} 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. The elements in the above set are the factors of 28.

Complete step-by-step answer:
The set given in the question is:
B = {1, 2, 4, 7, 14, 28}
If we look carefully at the elements of the above set, we will find all the elements are the factors of 28.
1 is a factor of 28.
2 is a factor of 28. On dividing 28 by 2 we get 14.
4 is a factor of 28. On dividing 28 by 4 we get 7.
7 is a factor of 28. On dividing 28 by 7 we get 4.
14 is a factor of 28. On dividing 28 by 14 we get 2.
28 is a factor of 28. On dividing 28 by 28 we get 1.
From the above discussion, we have shown that elements of the given set are the factors of 28.
So, the set – builder form of the given set B = {1, 2, 4, 7, 14, 28} is:
{x:$x\in N$and x is factor of 28}
In the above set – builder form, “N” represents natural numbers.
Hence, the set – builder form of the given set is {x: $x\in N$and x is a factor of 28}.

Note: We can write the elements of the set from the set – builder form as follows:
The set – builder form is given as:
{x:$x\in N$and x is factor of 28}
To find the elements of the set we need to factorize 28. All the factors of 28 are the elements of the set.
So, the factors of 28 are 1, 2, 4, 7, 14, 28.