Question

$1)$ Write the following sets in roster form

(i) $A=\{x:x\text{is an integer and}-3<x<7\}$

$2)$ Write the following sets in roster form

$\left(ii\right)$ $B=\{x:x\text{is a natural number less than}6\}$

$3)$ Write the following sets in roster form

$\left(iii\right)$ $C=\{x:x\text{is a two digit natural number such that the sum of its digits is}8\}$

$4)$ Write the following sets in roster form

$\left(iv\right)$ $D=\{x:x\text{is a prime number which is divisor of}60\}$

$5)$ Write the following sets in roster form

$\left(v\right)$ $E=$ The set of all letters in the world $\text{TRIGONOMETRY.}$

$6)$ Write the following sets in roster form

$\left(vi\right)$ $F=$The set of all letters in the word $\text{BETTER}$

Answer 1

$\left(i\right)$ Elements of the set $A$ are
$-2,-1,0,1,2,3,4,5,6$

Representaion in roster form,

$A=\{-2,-1,0,1,2,3,4,5,6\}$

$\left(ii\right)$ Elements of the set are $1,2,3,4,5,$

$\therefore$Representation in roster form,

$B=\{1,2,3,4,5\}$

$\left(iii\right)$ Elements of the set are $17,26,35,44,53,62,71$ and $80$

$\therefore$ Represtation in roster form,

$C=\{17,26,35,44,53,62,71,80\}$

$\left(iv\right)$ $\therefore 60=2\times 2\times 3\times 5$

So, elements of the set are $2,3,5$

$\therefore$Representaion in roster form,

$D=\{2,3,5\}$

$\left(v\right)$ in $\text{'TRIGONOMENTRY'}$ word, letters $\text{T.R.O}$ are repeated

So, letters in the set are $\text{T,R,I,G,O,N,M,E,Y}$

$\therefore$Representation in roster form,

$E=\left\{\text{T,R,I,G,O,N,M,E,Y}\right\}$


$\left(vi\right)$ $\text{'BETTER'}$ is a ${}^{\prime }{6}^{\prime }$ letter word out of which $E$ and $T$ are repeated,

$\therefore$ Representation in Roster form,

$F=\{B,E.T,R\}$