Exercise 1.1

1.           Which of the following are sets ? Justify.

          i) The collection of all the months of a year beginning with the letter J.

we can easily identify a month beginning with the letter J so this is a well defined collection of objects Hence, this collection is a set.

ii) The collection of ten most talented writers of India.

It is not a well-defined collection because the criteria for determining a talent may vary from person to person. Hence, this collection is not a set.           

     iii) Team of eleven best-cricket batsmen of the world.

 Criteria for determining a batsman’s talent may vary from person to person. Hence, this collection is not a set.

     iv) The collection of all boys in your class.

 The collection of all boys in your class is a well-defined collection because you can easily identify  a boy who belongs to this collection. Hence, Collection is a set.

     v) The collection of all natural numbers less than 100.

it is a well-defined collection because one can definitely identify a number that belongs to this collection. Hence, this collection is a set.

 vi)A collection of novels written by the writer Munshi Prem Chand.

           A collection of novels written by the writer Munshi Prem Chand is a well-defined collection and easily identify a book that belongs to this collection. Hence, this collection is a set.

           vii)The collection of all even integers.

 The collection of all even integers is a well-defined collection because one can definitely identify an even integer that belongs to this collection. Hence, this collection is a set.

viii)The collection of questions in this Chapter.

The collection of questions in this chapter is a well-defined collection because one can definitely identify a question that belongs to this chapter. Hence, this collection is a set.

  ix) A collection of most dangerous animals of the world.

It is not a well-defined collection because the criteria for determining the dangerousness of an animal can vary from animal to animal. Hence, this collection is not a set.

2.           Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces:

(i)     5. . .A                  (ii)    8 . . . A                  (iii) 0. . .A

 (iv)    4. . . A                 (v)   2. . .A                    (vi) 10. . .A

          (i) 5 ∈ A  (ii) 8 ∉ A  (iii) 0 ∉ A (iv) 4 ∈ A (v) 2 ∈ A  (vi) 10 ∉ A

3.           Write the following sets in roster form:

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

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

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

            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}

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

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

            D = {2, 3, 5}

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

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

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

        F = {B, E, T, R}

4.           Write the following sets in the set-builder form :

(i)   (3, 6, 9, 12}            (ii)   {2,4,8,16,32}              (iii) {5, 25, 125, 625}

(iv)    {2, 4, 6, . . .}         (v) {1,4,9, . . .,100}

1)    {x: x = 3n, n∈ N and 1 ≤ n ≤ 4}

2)    {x: x = 2ⁿ, n∈ N and 1 ≤ n ≤ 5}

3)    {x: x = 5ⁿ, n∈N and 1 ≤ n ≤ 4}

4)    {x: x is an even natural number}

5)    {x: x = n², n∈N and 1 ≤ n ≤ 10}

5.           List all the elements of the following sets :

(i)       A = {x : x is an odd natural number}

{1, 3, 5, 7, 9 …}           

                                                         

(ii)       B = {x : x is an integer, -1/2 < x < 4/2 }

Here x is a integer lies between -.5 and 4.5 hence B={0,1,2,3,4}

(iii)       C = {x : x is an integer, x² £ 4}

C = {–2, –1, 0, 1, 2}

(iv)       D = {x : x is a letter in the word “LOYAL”}

{L, O, Y, A}

(v)        E = {x : x is a month of a year not having 31 days}

 E= {February, April, June, September, November}

(vi)       F = {x : x is a consonant in the English alphabet which precedes k }.

 {b, c, d, f, g, h, j}

6.           Match each of the set on the left in the roster form with the same set on the right described in set-builder form:

(i)       {1, 2, 3, 6}            (a) {x : x is a prime number and a divisor of 6}

(ii)       {2, 3}                    (b) {x : x is an odd natural number less than 10}

(iii)       {M,A,T,H,E,I,C,S} (c) {x : x is natural number and divisor of 6}

(iv)       {1, 3, 5, 7, 9}         (d) {x : x is a letter of the word MATHEMATICS}.