HOW TO REPRESENT A SET IN ROSTER SET BUILDER AND DESCRIPTIVE FORMS

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 3³, 216 is the value of 6³

C  =  {4³, 5³}

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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