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

(i) $A=\{x:x\text{is an integer and}-3<x<7\}$
The elements of this set are $-2,-1,0,1,2,3,4,5,$ and $6$ only.
Therefore, the given set can be written in roster form as
$A=\{-2,-1,0,1,2,3,4,5,6\}$

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

The natural numbers less than $6$ are $1,2,3,4,5$
So, the elements of this set are $1,2,3,4,$ and $5$ only.
Therefore, the given set can be written in roster from as
$B=\{1,2,3,4,5\}$

(iii) $C=\{x:x\text{is a two-digit natural number such that the sum of its digits is 8}\}$
The elements of this set are $17,26,35,44,53,62,71$ and $80$ only.
Therefore, this set can be written in roster form as
$C=\{17,26,35,44,53,62,71,80\}$

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

$\underset{–}{2|60}$

$\underset{–}{2|30}$ $\underset{–}{3|15}$ $\underset{–}{5|5}$ $|1$

$\therefore 60=2\times 2\times 3\times 5$
$\therefore$ The elements of this set are $2,3$, and $5$ only.
Therefore, this set can be written in roster form as $D=\{2,3,5\}$.

(v) $E=$ The set of all letters in the word TRIGONOMETRY
There are $12$ letters in the word TRIGONOMETRY, out of which the letters, T, R, and O are repeated. And we write the repeated letters once only.
Therefore, this set can be written in roster form as
$E=\{T,R,I,G,O,N,M,E,Y\}$

(vi) $F=$ The set of all letters in the word BETTER
There are $6$ letters in the word BETTER, out of which letters E and T are repeated.
Therefore, this set can be written in roster form as
$F=\{B,E,T,R\}$