Q1. Write the following sets in the set builder form:
(i) The set E of days of the week.
(ii)The set A of natural numbers less than 20
(iii) The set of integers that lie between – 5 and 4 (both inclusive).
Q2. List the members of the following sets:
(i) {Odd numbers smaller
than 20}
(ii) {Numbers that differ from 6
by 1}
(iii) {The letters of the word ‘BLOOM’}
Q3. Fill in the blanks with the symbol
or
to make the statements true.
(i) 2… {set of odd numbers}
(ii) 0…. {5–5,5 + 5, 5 x 5, 5 ÷ 5}
(iii) r…. {p, e, n, c, i, l}
(iv) 1… {x: x is a prime number}
(v) papaya… {fruits}
Q4. List the elements of the given sets:
(i) {x: x is an integer and x2 = x}
(ii) {x: x is an even prime number}
(iii) A = {x: x
N and 4 < x < 12}
Q5. Which of the following are sets?
(i) A team of eleven best cricket batsmen of the world.
(ii) The collection of all even prime numbers.
(iii) The collection of all boys in your class.
(iv) A collection of most dangerous animals in the world.
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Q6. (i) Write the set A of the non-zero multiples of 3 less than 100
(ii) Write the set P of the integers greater than -6.
Q7. Write the following sets both in roster form and description form.
(i) {x: x = n2 x
N and n ≤ 7}
(ii){y: y = 2x -7, x
W and x<7}
Q8. A = {Prime numbers ≤ 19}. Insert the appropriate sign
(i) 4…A
(ii) 7…A
(iii) 9…A
(iv) 13…A
or
in the blank spaces.
(v) 1…A
Q9. Specify each of the following sets by stating a rule:
(i) {15, 16, 17, 18, 19…}
(ii) {7, 14, 21, 28, 35, 42…}
(iii) {- 5, - 3, - 1, - 2, - 4}
Q10. Specify each of the following sets in set builder form:
(i) A = {4, 8, 12, 16, 20, 24…}
(ii) B = {8, 27, 64, 125, 216…}
(iii) C = {…, - 4, - 3, - 2, - 1, 0}
Q11. State the cardinal number of the following sets:
(i) P = {Planets of our solar system}
(ii) A = {x: x + 3 = 0, x
N}
(iii) B = {set of numbers whose square is 81}
Q12. Write each of the following sets in Roster form;
(i) The set of prime numbers less than 25
(ii) The set of colors of the rainbow.
(iii) The set of letters in the word ‘BHARAT’.
Q13. If X = {2, 5, 8, 14, 17, 20, 25} and A = {x: x
tabular form of A.
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X, x is divisible by 5}, then find the
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Q14. Rewrite the following sets in roster form;
(i) {x: x is a letter in the word ‘Remember’}
(ii) {x: x > 0 and x2 = 49}
Q15. The description of the sets is given below is followed by a list. Identify the members of
the set described from the given list.
(i) The set of Presidents of India.
Lord Mountbatten; Shri Rajendra Prasad; Shri C. Raja Gopalachari; Dr. Radha Krishnan;
Dr. Zakir Husain.
(ii) The set of persons in India who have won the Nobel Prize.
Dr.C. V Raman; Rabindra Nath Tagore; Shri J. L Nehru; Mahatma Gandhi; Shri Bal
GangadharTilak
Q16. List all the elements of the following sets;
(i) B = {x: x is an integer,
1
2
x<
9
}
2
(ii) F = {x: x is a consonant in the English alphabet which precedes ‘k’}
Q17. Match each 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 natural number and a divisor of 30}
(ii) {2, 3, 5, 6, 10, 15, 30}
(b) {x: x is a prime number less than 20}
(iii) {M, A, T, H, E, I, C, S}
( c) {x: x is a natural number and divisor of 6}
(iv) {2, 3, 5, 7, 11, 13, 17, 19}
(d) {x: x is a letter of the word ‘MATHEMATICS’}
Q18. Rewrite the given sets in the roster form;
(i) {x:x is an integer and x+1=0}
(ii){x: x is a positive integer and is a divisor of 18}
Q19. Write the set
1 2 3 4 5 6
, , , , , in the set builder form.
2 3 4 5 6 7
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Q20. In the following, state whether A = B or not; give reason:
(i) A = {1, 2, 3, 4} B = {4,3,1,2}
(ii) A= {4, 8, 12, 16} B = {8,4,16,18}
(iii) A = {2, 4, 6, 8, 10} B = {x: x is a positive even integer ≤ 10}
(iv) A = {x: x is a multiple of 10} B = {10, 15, 20, 25, 30…]
Answers:
A1.
(i) E ={x: x is the day of the week}
(ii) A = {x: x N, x < 20}
(iii) {x: x
Z, - 5 ≤ x ≤ 4}
A2. (i) {1,3, 5,7,9,11,13,15,17,19}
(ii) {5, 7}
(iii) {B, L, O, M}
A3. (i)
(ii)
(iii)
(iv)
(v)
A4. (i) {1}
(ii) {2}
(iii) {5, 6, 7, 8, 9, 10, 11}
A5. (i) Not a well defined collection, hence not a set.
(ii) It is a well defined collection, hence it is a set.
(iii) It is a well defined collection, hence it is a set.
(iv) Not a well defined collection, hence not a set.
A6. (i) The set of non-zero multiples of 3 less than 100 is A = {3, 6, 12, 15, 18…..99}
(ii) P = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7…}
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A7. (i) Roster form of the given set is: {1, 4, 9, 16, 25, 36, 49}
Description form: {squares of first seven natural numbers}
(ii) Roster form of the given set is: {- 7, - 5, - 3, - 1, 1, 3, 5}
Description form: {set of odd integers lying between – 8 and 6}
A8. (i)
(ii)
(iii)
(iv)
(v)
A9. (i) Set of natural numbers greater than 14.
(ii) The set of positive integers that are multiples of 7.
(iii)The set of negative integers between 0 and – 6.
A10. (i) A = {x: x = 4n n
(ii) B = {x:x = n3 n
N}
N, n > 1}
(iii) C = {x: x ≤ 0, x
Z}
A11. (i) 8 (ii) 0 (iii) 2
A12. (i) A = {2, 3, 5, 7, 11, 13, 17, 19, 23}
(ii) B = {Violet, Indigo, Blue, Green, Yellow, Orange, Red}
(iii) C = {B, H, A, R, T}
A13. The tabular form of a ={5,20, 25}
A14. (i) {R, E, M, B}
(ii) {7}
A15. (i) The members of the given set: Presidents of India are:
Dr. Rajendra Prasad, Dr. Radha Krishnan, Dr. Zakir Husain.
(ii) The members of the given set: Persons who won the Nobel Prize are:
Dr. C. V Raman, Rabindra Nath Tagore
A16.(i) B = {0, 1, 2, 3, 4}
(ii) F = {b, c, d, f, g, h, j}
A17. (i) ↔ ( c) (ii) ↔ (a)
(iii) ↔ (d)
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(iv) ↔ (b)
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A18. (i) {0} (ii) {1, 2, 3, 6, 9, 18}
A19. A
x: x=
n
, where n is a natural number and1 n 6
n+1
A20.(i) Since A and B have exactly the same elements, hence we can say that A = B.
(ii) Since A and B do not have the same elements, they are not equal. (12 and 18 are
different)
(iii) A and B have exactly the same elements, hence they are equal. A = B
(iv) A and B do not have the same elements therefore A is not equal to B.
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