A = {x: x is an integer and –3 < x < 7}

(i) Given that,

A = {x: x is an integer and –3 < x < 7}

To write the above expression in its roaster form

In roaster form, the order in which the elements are listed is immaterial.

The elements of the set are −2,−1,0,1,2,3,4,5,6.

The roaster form of the set A = {x: x is an integer and –3 < x < 7} is

A = {–2, –1, 0, 1, 2, 3, 4, 5, 6}

(ii) Given that,

B =  {x: x is a natural number less than 6}

To write the above expression in its roaster form

In roaster form, the order in which the elements are listed is immaterial.

The elements of the set are 1,2,3,4,5.

The roaster form of the set B =  {x: x is a natural number less than 6} is 

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

(iii) Given that,

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

To write the above expression in its roaster form

In roaster form, the order in which the elements are listed is immaterial.

The elements of the set are 17,26,35,44,53,62,71,80 such that their sum is 8 The roaster form of the set

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

is  {17, 26, 35, 44, 53, 62, 71, 80}.

(iv) Given that,

D ={x: x is a prime number which is divisor of 60}

To write the above expression in its roaster form

In roaster form, the order in which the elements are listed is immaterial.

The divisors of 60 are 2,3,4,5,6. Among these the prime numbers are 2,3,5

The elements of the set are 2,3,5.

The roaster form of the set D = {x: x is a prime number which is divisor of 60}

is D = {2, 3, 5}.

(v) E= The set of all letters in the word TRIGONOMETRY

Given that,

E =The set of all letters in the word TRIGONOMETRY

To write the above expression in its roaster form

In roaster form, the order in which the elements are listed is immaterial.

There are 12 letters in the word TRIGONOMETRY out of which T, R and O gets repeated.

The elements of the set are T, R, I G, O, N, M, E, Y.

The roaster form of the set E =The set of all letters in the word

TRIGONOMETRY is E = {T, R, I, G, O, N, M, E, Y}.

(vi) F =The set of all letters in the word BETTER

Given that,

F =The set of all letters in the word BETTER

To write the above expression in its roaster form

In roaster form, the order in which the elements are listed is immaterial.

There are 6 letters in the word BETTER out of which E and T are repeated.

The elements of the set are B, E, T, R.

The roaster form of the set F =The set of all letters in the word BETTER is
F = {B, E, T, R}