Question

please answer in your notebook​

Answer 1

$\large\underline{\sf{Given \:Question - }}$

$\sf \: Write \: the \: set \: A \: = \bigg\{\dfrac{1}{3} ,\dfrac{1}{2}, \dfrac{3}{5}, \dfrac{2}{3} ,\dfrac{5}{7}, \dfrac{3}{4}, \dfrac{7}{9} \:\bigg\} \: in \: set \: builder \: form$

$\large\underline{\sf{Solution-}}$

Given

$\rm :\longmapsto\:A \: = \bigg\{\dfrac{1}{3} ,\dfrac{1}{2}, \dfrac{3}{5}, \dfrac{2}{3} ,\dfrac{5}{7}, \dfrac{3}{4}, \dfrac{7}{9} \:\bigg\}$

Set A can be rewritten as

$\rm :\longmapsto\:A \: = \bigg\{\dfrac{1}{3} ,\dfrac{2}{4}, \dfrac{3}{5}, \dfrac{4}{6} ,\dfrac{5}{7}, \dfrac{6}{8}, \dfrac{7}{9} \:\bigg\}$

$\rm :\longmapsto\:A \: = \bigg\{\dfrac{1}{1 + 2} ,\dfrac{2}{2 + 2}, \dfrac{3}{3 + 2}, \dfrac{4}{4 + 2} ,\dfrac{5}{5 + 2}, \dfrac{6}{6 + 2}, \dfrac{7}{7 + 2} \:\bigg\}$

Thus, we got a pattern,

So,

Set Builder form is

$\rm :\longmapsto\: A = \bigg\{ \: x : x \: = \: \dfrac{n}{n + 2} , \: n \in \: N \: and \: 1 \leqslant n \leqslant 7 \bigg\}$

Basic Concept :-

Set :- Sets are represented as a collection of well-defined objects or elements

Representation of Sets

The sets are represented in curly braces, {}.

The elements in the sets are depicted in three forms

• Statement form

• Roster Form

• Set Builder Form.

Statement Form

• In statement form, the well-defined descriptions of a member of a set are written and enclosed in the curly brackets.

• For example, the set of odd numbers less than 10. In statement form, it can be written as A = {odd numbers less than 10}.

Roster Form

• In Roster form, all the elements of a set are listed in row, separated by commas and enclosed in { }.

• For example, the set of natural numbers less than 9. In roster form, it is written as A = {1, 2, 3, 4, 5, 6, 7, 8}

Set Builder Form

• The general form is, A = { x : property}

Answer 2

Solution

A={ 31 , 21 ,53 , 32 , 75 , 43 , 97}

Set A can be rewritten as

$\rm :\longmapsto\:A \: = \bigg\{\dfrac{1}{3} ,\dfrac{2}{4}, \dfrac{3}{5}, \dfrac{4}{6} ,\dfrac{5}{7}, \dfrac{6}{8}, \dfrac{7}{9} \:\bigg\}:⟼$

A={ 31, 42 , 53, 64 ,75, 86, 97}

$\rm :\longmapsto\:A \: = \bigg\{\dfrac{1}{1 + 2} ,\dfrac{2}{2 + 2}, \dfrac{3}{3 + 2}, \dfrac{4}{4 + 2} ,\dfrac{5}{5 + 2}, \dfrac{6}{6 + 2}, \dfrac{7}{7 + 2} \:\bigg\}:⟼$

A={ 1+21 , 2+22, 3+23, 4+24, 5+25, 6+26, 7+27 }

Thus, we got a pattern,

So,

Set Builder form is

$\rm :\longmapsto\: A = \bigg\{ \: x : x \: = \: \dfrac{n}{n + 2} , \: n \in \: N \: and \: 1 \leqslant n \leqslant 7 \bigg\}$

${Basic Concept}$

Set :- Sets are represented as a collection of well-defined objects or elements

Representation of Sets

The sets are represented in curly braces, {}.

The elements in the sets are depicted in three forms

Statement form

Roster Form

Set Builder Form.

Statement Form

In statement form, the well-defined descriptions of a member of a set are written and enclosed in the curly brackets.

For example, the set of odd numbers less than 10. In statement form, it can be written as A = {odd numbers less than 10}.

Roster Form

In Roster form, all the elements of a set are listed in row, separated by commas and enclosed in { }.

For example, the set of natural numbers less than 9. In roster form, it is written as A = {1, 2, 3, 4, 5, 6, 7, 8}

Set Builder Form

The general form is, A = { x : property}