Question

If A 3.9.27.81 then write A in the set builder form

Answer 1

Answer:

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Answer 2

Basic Concept :-

Set Builder Form :-

• In the set builder form, every elements of the set, must possess a property to become the member of that set. The set A = {x : x is a vowel} is read as "The set A equals to x such that x is a vowel."

Let's solve the problem now!!!

Given Question :-

If A = {3, 9, 27, 81}, then write A in set builder form.

Solution :-

Given set is

$\rm :\longmapsto\:A \: = \: \{3, 9, 27, 81 \}$

Let first make a pattern

$\rm :\longmapsto\:A \: = \: \{3,{3}^{2}, {3}^{3},{3}^{4}\}$

So,

Set builder form is

$\rm :\longmapsto\:A \: = \: \{x : x = {3}^{n}, \: n \in \: N \: and \: n \leqslant 4 \}$

Additional Information :-

Let solve few more problems

Example :- 1

Express in set builder form :-

$\rm :\longmapsto\:A \: = \: \{1, 4, 9, 16, \: - - - \}$

Solution :-

Let first make a pattern

$\rm :\longmapsto\:A \: = \: \{ {1}^{2} , {2}^{2} , {3}^{2} , {4}^{2} , \: - - - \}$

So,

Set Builder Form is

$\rm :\longmapsto\:A \: = \: \{x : x = {n}^{2}, \: n \in \: N \}$

Example :- 2

Express in Set builder form:-

$\rm :\longmapsto\:A \: = \: \ \bigg \{ \dfrac{1}{2} , \dfrac{2}{3} , \dfrac{3}{4} , \dfrac{4}{5} , \: - - \dfrac{7}{8} \bigg \}$

Solution :-

Let first make a pattern

$\rm :\longmapsto\:A \: = \: \ \bigg \{ \dfrac{1}{1 + 1} , \dfrac{2}{2 + 1} , \dfrac{3}{3 + 1} , \dfrac{4}{4 + 1} , \: - - \dfrac{7}{7 + 1} \bigg \}$

So,

Set builder form is

$\rm :\longmapsto\:A \: = \: \ \bigg \{ x : \: x \: = \: \dfrac{n}{n + 1}, \: n \in \: N \: and \: n \leqslant 7\bigg \}$