Exercise 1

1. Which of the following are sets? Justify your answer?

(i) The collection of all the months of a year begining with the letter “J”.

Set. Because it is well defined.Thus the set is {January,June,July}

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

Not a set. It is not defined well.

(iii) A team of eleven best cricket batsmen of the world.

Not a set.It is not defined well.

(iv) The collection of all boys in your class.

Set. It is defined well.

(v) The collection of all even integers.

Set. It is well defined. The set is {2,4,6,8,----}

(vi) All even numbers

Set. it is well defined and the set is {2,4,6,8,10,----}

(vii) Stars in the sky

Not a set. It is undefined.

(viii) The collection of odd positive integers. 1, 3, 5, …..

Set.It is well defined and the set is {1,3,5,7,----}

2. If A={0, 2, 4, 6}, B = {3, 5, 7} and C = {p, q, r}then fill the appropriate symbol, ∈ or ∉ in the blanks.

(i) 0 ….. A (ii) 3 ….. C (iii) 4 ….. B

(iv) 8 ….. A (v) p ….. C (vi) 7 ….. B

Solution:

(i) 0 ∈ A (ii) 3 ∉ C (iii) 4 ∉ B

(iv) 8 ∉ A (v) p ∈ C (vi) 7 ∈ B

3. Express the following statements using symbols.

(i) The element ‘x’ does not belong to ‘A’.

x ∉ A

(ii) ‘d’ is an element of the set ‘B’.

d ∈ B

(iii) ‘1’ belongs to the set of Natural numbers N.

1 ∈ N

(iv) ‘8’ does not belong to the set of prime numbers P.

8 ∉ P

4. State whether the following statements are true or false.

(i) 5 ∉{Prime numbers}

False.5 is a prime number

(ii) S = {5, 6, 7} implies 8 ∈ S.

False. 8 not belongs to S

(iii) -5 ∉ W where‘W’ is the set of whole numbers

True. -5 is a negative integer.Whole numbers are starting from 0.

(iv) `8/11` ∈ Z where ‘Z’ is the set of integers.

False.`8/11` is a rational number.

5. Write the following sets in roster form.

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

B={1,2,3,4,5,6}

(ii) 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}

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

D={2,3,5}

(iv) E = {the set of all letters in the word BETTER}.

E={B,E,T,R}

Do this:

1.List the elements of the following sets.

(i) G = all the factors of 20

{1,2,4,5,10,20}

(ii) F = the multiples of 4 between 17 and 61 which are divisible by 7

{20,24,28,32,36,40,44,48,52,56,60}

(iii) S = {x : x is a letter in the word 'MADAM'}

{M,A,D}

(iv) P = {x : x is a whole number between 3.5 and 6.7}

{4,5,6}

2. Write the following sets in the roster form.

(i) B is the set of all months in a year having 30 days.

{april,june,september,november}

(ii) P is the set of all prime numbers less than 10.

{2,3,5,7}

(iii) X is the set of the colours of the rainbow

{violet,blue,green,yellow,orange,red}

6. Write the following sets in the set-builder form.

(i) {3, 6, 9, 12}

{x:x is a multiple of 3 less than 15}

(ii) {2, 4, 8, 16, 32}

{x:x=2ⁿ, n∈ N and n is less than 6}

(iii) {5, 25, 125, 625}

{x:x=5ⁿ, n∈ N and n is less than 5}

(iv) {1, 4, 9, 25, ….. 100}

{x:x is a square number less than 101}

(v){P, R, I, N, C, A, L}

{x : x is a letter of the word PRINCIPAL}

(vi){0}

{x : x is an integer and x + 1 = 1}

(vii) {1, 2, 3, 6, 9, 18}

{x : x is a positive integer and is a divisor of 18}

(viii) {3, -3}

{x : x is an integer and x² – 9 = 0}

7. List all the elements of the following sets in roster form.

(i) A = {x : x is a natural number greater than 50 but less than 100}

{51,52,53,----------,99}

(ii) B = {x : x is an integer, x² = 4}

{2}

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

{L,O,Y,A}

8. Match the roster form with set-builder form.

Solution:

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❮ Types of sets