Question

Write the set A = {1, 2, 3, 4, 5, 6, 7} in the set – builder form.

Answer 1

Hint: Set – builder form is a general notation to write the elements of the set which describes the properties of the elements of the set. We can see from the above set that 1 to 7 are natural numbers.

Complete step-by-step answer:
The set A given in the question is:
A = {1, 2, 3, 4, 5, 6, 7}
We can see that elements of the above set are consecutive numbers starting from 1 and ending to 7. We know that 1, 2, 3, 4, 5, 6……… are natural numbers so we can say that the above numbers are natural numbers from 1 to 7.
The set – builder form of the given set A = {1, 2, 3, 4, 5, 6, 7} is:
{x: n where $n\in N$ and 1≤n≤7}
In the above set – builder form “N” represents natural numbers and the inequality 1≤n≤7 represents that n can take value from 1 to 7.
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 n then describe what n is. Make sure to write the whole set – builder form in the curly brackets.
Hence, the set – builder form of the given set is {x: n where $n\in N$and 1≤n≤7}.

Note: If in some question, part of the question is given in set – builder form and the other part uses this information of set – builder so we need to know how to read a set – builder form.
The set – builder form:
{x: n where $n\in N$ and 1≤n≤7}
From the above set – builder form, the inequality shows that n is from 1 to 7. Now,
Plugging n = 1 in n we get the first element as 1.
Plugging n = 2 in n we get the second element as 2.
Plugging n = 3 in n we get the third element as 3.
Likewise, we can find the value of a set of the elements till 7.