Question

Write the following sets in roster form:
(i) $A\{x:x\text{is an integer and}-3<x<7\}$
(ii) $B=\{x:x\text{is a natural number less than 6}\}$
(iii) $C=\{x:x\text{is a two-digit natural such that the sum of its digits is 8}\}$
(iv) $D=\{x:x\text{is a prime number which is divisor of 60}\}$
(v) $E=$ The set of all letters in the word TRIGONOMETRY.
(vi) $F=$ The set of all letters in the word BETTER.

Answer 1

$\left(i\right)$ Integers lying between $-3$ and $7$ are
$-2,-1,0,1,2,3,4,5,6$
$\therefore$ Representation in roster form
$A=\{-2,-1,0,1,2,3,4,5,6\}$

$\left(ii\right)$ Natural numbers less than $6$ are $1,2,3,4,5$
$\therefore$ Representation in roster form
$B=\{1,2,3,4,5\}$

$\left(iii\right)$ Two digit numbers whose sum of digits is $8$ are $17,26,35,44,53,62,71$ and $80$
$\therefore$ Representation in roster from
$C=\{17,26,35,44,53,62,71,80\}$

$\left(iv\right)$ $\because 60=2\times 2\times 3\times 5$
So, elemnets of the set are $2,3,5$
$\therefore$ Representation in roster form
$D=\{2,3,5\}$

$\left(v\right)$ In the word $"TRIGONOMETR{Y}^{\prime \prime }$, letters $T,R,O$ are repeated
So, letters in the set are $T,R,I,G,O,N,M,E,Y$
$\therefore$ Representation in roster form
$E=\{T,R,I,G,O,N,M,E,Y\}$

$\left(vi\right)$ $BETTER$ is a $6$ letter word out of which $E$ and $T$ are repeated
$\therefore$ Representation in roster form
$F=\{B,E,T,R\}$