1. Which of the following are sets ? Justify your answer.
(i) The collection of all the months of a year beginning with the letter J.
All months starting with letter J can be definitely identified. So this collection of objects is well defined. Hence, this collection is a set.
(ii) The collection of ten most talented writers of India.
The parameter for determining the talented writers vary from person to person. So this collection is not well defined. Hence, this collection is not a set.
(iii) A team of eleven best-cricket batsmen of the world.
The parameter for determining the best-cricket batsmen vary from person to person. So this collection is not well defined. Hence, this collection is not a set.
(iv) The collection of all boys in your class.
A boy belonging to this collection can be definitely identified because the collection of all boys in your class is well defined. Hence, this collection is a set.
(v) The collection of all natural numbers less than 100.
A number belonging to this collection can be definitely identified because the collection of all natural numbers less than 100 is well defined. Hence, this collection is a set.
(vi) A collection of novels written by the writer Munshi Prem Chand.
A book belonging to this collection can be definitely identified because the collection of all novels written by Munshi Prem Chand is well defined. Hence, this collection is a set.
(vii) The collection of all even integers.
A number belonging to this collection can be definitely identified because the collection of all even integers is well defined. Hence, this collection is a set.
(viii) The collection of questions in this Chapter.
A question belonging to this collection can be definitely identified because the collection of questions in this chapter is well defined. Hence, this collection is a set.
(ix) A collection of most dangerous animals of the world.
The parameter for determining the most dangerous animals vary from person to person. So this collection is not well defined. 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}
x is greater than or equal to -3. So -3 is must be included.
x is less than 7. So 7 is should not be included.
A={-3,-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}
60=2*2*3*5
D={2,3,5}
(v) E = The set of all letters in the word TRIGONOMETRY
T, R, O are repeated
E={T,R,I,G,O,N,M,E,Y}
(vi) F = The set of all letters in the word BETTER
E,T are repeated
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}
(i) {3, 6, 9, 12} = {x: x=3n, n∈N, 1≤n≤4}
(ii) {2,4,8,16,32}
Here, $\displaystyle \small 2^{1}=2$, $\displaystyle \small 2^{2}=4$, $\displaystyle \small 2^{3}=8$, $\displaystyle \small 2^{4}=16$, $\displaystyle \small 2^{5}=32$
hence, {2,4,8,16,32} ={x: x=$\displaystyle \small 2^{n}$, n∈N, 1≤n≤5}
(iii) {5, 25, 125, 625}
Here, $\displaystyle \small 5^{1}=5$, $\displaystyle \small 5^{2}=25$, $\displaystyle \small 5^{3}=125$, $\displaystyle \small 5^{4}=625$
Hence, {5, 25, 125, 625}={x: x=$\displaystyle \small 5^{n}$, n∈N, 1≤n≤4}
(iv) {2, 4, 6, . . .}
It is a set of all even natural numbers
Hence, {2, 4, 6, . . .}={x: x is an even natural number}
(v) {1,4,9, . . .,100}
Here, $\displaystyle \small 1^{2}=1$, $\displaystyle \small 2^{2}=4$, $\displaystyle \small 3^{2}=9$......$\displaystyle \small 10^{2}=100$
Hence, {1,4,9, . . .,100}={x: x =$\displaystyle \small n^{2}$, n∈N, 1≤n≤10}
5. List all the elements of the following sets
(i) A = {x : x is an odd natural number}
A={1,3,5,7,9.......}
(ii) B={x: x is an integer, -(1/2)<x<(9/2)}
B={0,1,2,3,4}
(iii) C = {x : x is an integer, $\displaystyle \small x^{2}$ ≤ 4}
C={-2,-1,0,1,2}
(iv) D = {x : x is a letter in the word “LOYAL”}
D={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 }
F={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}
(i) {1, 2, 3, 6} (c) {x : x is natural number and divisor of 6}
(ii) {2, 3} (a) {x : x is a prime number and a divisor of 6}
(iii) {M,A,T,H,E,I,C,S} (d) {x : x is a letter of the word MATHEMATICS}
(iv) {1, 3, 5, 7, 9} (b) {x : x is an odd natural number less than 10}
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