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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.
Just scribble down the discrete elements within 2nd bracket
1.-2 -1 0 1 2 3 4 5 6
2. 1 2 3 4 5
3. 1 + 7 starting with min natural no this 71 and 17
2 + 6 gives 26 62
3 + 5 gives 35 53
4 + 4 gives degenerate 44
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){x:x=3n,1≤n≤4,n∈Z}
(ii){x:x=,1≤n≤5,n∈Z}
(iii){x:x=,1≤n≤4,n∈Z}
(iv){x:x is an even natural number}
(v){x:x=,1≤n≤10,n∈Z}
Which of the following are sets? Justify our answer.
(i) The collection of all months of a year beginning with the letter J.
(ii) The collection of ten most talented writers of India.
(iii) A team of eleven best-cricket batsmen of the world.
(iv) The collection of all boys in your class.
(v) The collection of all natural numbers less than 100.
(vi) A collection of novels written by the writer Munshi Prem Chand.
(vii) The collection of all even integers.
(viii) The collection of questions in this Chapter.
(ix) A collection of most dangerous animals of the world.
A set is a well defined collection of objects,numbers and things.
(i)set
because it's a well defined collection of months. one can definitely identify this collection.
(ii) Not a set
criteria for selecting talented writers varies from person to person. not a well defined collection
(iii)NOt a set
criteria for selecting best cricketers varies from person to person. not a well defined collection
(iv)set
Countable and well defined
(v)set
countable and well defined
(vi)set
well defined collection
(vii)Set
well defined collection
(viii)set
well defined collection
(ix)Set
varies from person to person
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)∈
(ii)∉
(iii)∉
(iv)∈
(v)∈
(vi)∉
List all the elements of the following sets:
(i) A = {x: x is an odd natural number}
(ii) B = {x: x is an integer,
}
(iii) C = {x: x is an integer,
}
(iv) D = {x: x is a letter in the word “LOYAL”}
(v) E = {x: x is a month of a year not having 31 days}
(vi) F = {x: x is a consonant in the English alphabet which proceeds k}.
(i) A = {x: x is an odd natural number} = {1, 3, 5, 7, 9 …}
(ii) B = {x: x is an integer;
}
It can be seen that 
and 
∴ B 
(iii) C = {x: x is an integer;}
It can be seen that
(–1)2 = 1 ≤ 4; (–2)2 = 4 ≤ 4; (–3)2 = 9 > 4
02 = 0 ≤ 4
12 = 1 ≤ 4
22 = 4 ≤ 4
32 = 9 > 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}
= {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}
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) All the elements of this set are natural numbers as well as the divisors of 6. Therefore, (i) matches with (c).
(ii) It can be seen that 2 and 3 are prime numbers. They are also the divisors of 6.
Therefore, (ii) matches with (a).
(iii) All the elements of this set are letters of the word MATHEMATICS. Therefore, (iii) matches with (d).
(iv) All the elements of this set are odd natural numbers less than 10. Therefore, (iv) matches with (b).
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