Write the following sets in roster form:
(i) A = {x : x is an integer and –3 ≤ x < 7}
(ii) B = {x : x is a natural number less than 6}
(iii) C = {x : x is a two-digit natural number such that the sum of its digits is 8}
(iv) D = {x : x 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

Solution:

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

The elements of this set are - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, and 6 only.

Therefore, the given set can be written in roster form as

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

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

The elements of this set are 1, 2, 3, 4, and 5 only.

Therefore, the given set can be written in roster form as B = {1, 2, 3, 4, 5}

(iii) C = { x: x 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 is a prime number which is a divisor of 60}

2 |60

2 |30

3 |15

    |5

Hence, 60 = 2 x 2 x 3 x 5

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 letters T, R, and O are repeated.

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}

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NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.1 Question 3

Write the following sets in roster form: (i) A = {x : x is an integer and –3 ≤ x < 7} (ii) B = {x : x is a natural number less than 6} (iii) C = {x : x is a two-digit natural number such that the sum of its digits is 8} (iv) D = {x : x 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

Solution:

We are asked to write the given sets in roaster form. We found that
(i) A = { x : x is an integer and - 3 ≤ x < 7 } = {- 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6}
(ii) B = { x : x is a natural number less than 6} = {1, 2, 3, 4, 5}
(iii) C = { x : x is a two-digit natural number such that the sum of its digits is 8} =  {17, 26, 35, 44, 53, 62, 71, 80}
(iv) D = { x : x is a prime number which is divisor of 60} = {2, 3, 5}
(v) E = The set of all letters in the word TRIGONOMETRY = {T , R, I , G, O, N , M , E, Y}
(vi) F = The set of all letters in the word BETTER = {B, E, T, R}