Question

[tex] \large \purple \bigstar \: \color{red} \boxed{ \sf\color{maroon}{Quality \: Question : }}[\tex] If there is a set A and A={1,-2,4,-8....}, then write it in set builder form​

Answer 1

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 = {1, - 2, 4, - 8, - - -}, then write A in set builder form.

Solution :-

Given set is

$\rm :\longmapsto\:A = \{1, - 2,4, - 8, - - - \}$

Let first make a pattern.

$\rm :\longmapsto\:A = \{ {2}^{0} , - {2}^{1} , {2}^{2} , - {2}^{3} , - - - \}$

$\rm :\longmapsto\:A = \{ {( - 2)}^{0} , {( - 2)}^{1} , {( - 2)}^{2} , {( - 2)}^{3} , - - - \}$

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

So,

Set Builder Form is

$\red{\bf :\longmapsto\:A = \{x : x = {( - 2)}^{n - 1}, \: n \in \: N \}}$

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

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

Example :- 2

Express in set builder form :-

$\rm :\longmapsto\:A \: = \: \{2, 4, 6, 8, \: - - - \}$

Solution :-

Let first make a pattern

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

So,

Set Builder Form is

$\green{\bf :\longmapsto\:A = \{x : x = {2n}, \: n \in \: N \}}$