Question 1 :
Represent the following sets in Roster form.
(i) A = The set of all even natural numbers less than 20.
Answer :
The given set will contain even natural numbers lesser than 20.
A = {2, 4, 6, 8, 10, 12, 14, 16, 18}
(ii) B = {y : y = 1/2n , n ∈ N, n ≤ 5}
Solution :
B = {y : y = 1/2n , n ∈ N, n ≤ 5}
If n = 1, then y = 1/2
If n = 2, then y = 1/4
If n = 3, then y = 1/6
If n = 4, then y = 1/8
If n = 5, then y = 1/10
B = { 1/2, 1/4, 1/6, 1/8, 1/10 }
(iii) C = {x : x is perfect cube, 27 < x < 216}
Answer :
27 is the value of 3^{3}, 216 is the value of 6^{3}
C = {4^{3}, 5^{3}}
C = {64, 125}
(iv) D = {x : x ∈ Z, –5 < x ≤ 2}
Answer :
D = {-4, -3, -2, -1, 0, 1, 2}
Question 2 :
Represent the following sets in set builder form.
(i) B = The set of all Cricket players in India who scored double centuries in One Day Internationals.
Answer :
B = {x : x is an Indian player who scored double centuries in One Day International}
(ii) C = {1/2, 2/3, 3/4, ..........}
Answer :
By observing the given set, the denominator is 1 greater than the numerator.
C = {x : x = n/(n + 1) where n ∈ N}
(iii) D = The set of all tamil months in a year.
Answer :
D = {x : x is the set of all tamil months in a year.}
(iv) E = The set of odd Whole numbers less than 9.
Answer :
E = {x: x is the set of odd Whole numbers less than 9}
Question 3 :
Represent the following sets in descriptive form.
(i) P = { January, June, July}
Answer :
P = The set of English months starting with J
(ii) Q = {7, 11, 13, 17, 19, 23, 29}
Answer :
Q = the set of prime numbers between 5 and 31.
(iii) R = {x : x ∈ N, x < 5}
Answer :
R = The set of natural numbers less than 5.
(iv) S = {x : x is a consonant in English alphabets}
Answer :
S = The set of consonants in English alphabets
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