Write each of the following sets in the Roster Form:
(i) The set of five numbers each of which is divisible by 3.
(ii) The set of integers between -4 and 4.
(iii) { x : x is a letter in the word 'SCHOOL' }
(iv) { x : x is an odd natural number between 10 and 20 }
(v) { Vowels used in the word 'AMERICA' }
(vi) { Consonants used in the word 'MADRAS' }
Answer
(i) Five numbers each divisible by 3 are 3, 6, 9, 12 and 15.
The required set = { 3, 6, 9, 12, 15 }
(ii) The integers between -4 and 4 are -3, -2, -1, 0, 1, 2 and 3.
The required set = { -3, -2, -1, 0, 1, 2, 3 }
(iii) The letters in the word 'SCHOOL' are S, C, H, O, O, L. Writing each letter only once, we get S, C, H, O, L.
{ x : x is a letter in the word 'SCHOOL' } = { s, c, h, o, l }
(iv) The odd natural numbers between 10 and 20 are 11, 13, 15, 17 and 19.
{ x : x is an odd natural number between 10 and 20 } = { 11, 13, 15, 17, 19 }
(v) The vowels used in the word 'AMERICA' are A, E, I, A. Writing each vowel only once, we get A, E, I.
{ Vowels used in the word 'AMERICA' } = { a, e, i }
(vi) The consonants used in the word 'MADRAS' are M, D, R, S.
{ Consonants used in the word 'MADRAS' } = { m, d, r, s }
Write each given set in the Roster Form:
(i) All prime numbers between 1 and 20.
(ii) The squares of the first four natural numbers.
(iii) Even numbers between 1 and 9.
(iv) The first eight letters of the English alphabet.
(v) The letters of the word 'BASKET'.
(vi) Four cities of India whose names start with the letter J.
(vii) Any four closed geometrical figures.
(viii) Vowels used in the word 'MONDAY'.
(ix) Single digit numbers that are perfect squares as well.
Answer
(i) The prime numbers between 1 and 20 are 2, 3, 5, 7, 11, 13, 17 and 19.
The required set = { 2, 3, 5, 7, 11, 13, 17, 19 }
(ii) The first four natural numbers are 1, 2, 3 and 4. Their squares are 12 = 1, 22 = 4, 32 = 9 and 42 = 16.
The required set = {12, 22, 32, 42} = { 1, 4, 9, 16 }
(iii) The even numbers between 1 and 9 are 2, 4, 6 and 8.
The required set = { 2, 4, 6, 8 }
(iv) The first eight letters of the English alphabet are a, b, c, d, e, f, g and h.
The required set = { a, b, c, d, e, f, g, h }
(v) The letters of the word 'BASKET' are B, A, S, K, E, T.
The required set = { b, a, s, k, e, t }
(vi) Four cities of India whose names start with the letter J are Jaipur, Jodhpur, Jalandhar and Jhansi.
The required set = { Jaipur, Jodhpur, Jalandhar, Jhansi }
(vii) Four closed geometrical figures are a triangle, a circle, a parallelogram and a pentagon. (Any four such figures may be taken.)
The required set = { triangle, circle, parallelogram, pentagon }
(viii) The vowels used in the word 'MONDAY' are O and A.
The required set = { o, a }
(ix) The single digit numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Out of these, the perfect squares are 0, 1, 4 and 9, since 0 = 02, 1 = 12, 4 = 22 and 9 = 32.
The required set = { 0, 1, 4, 9 }
Write each given set in the Set-Builder Form:
(i) { 2, 4, 6, 8, 10 }
(ii) { 2, 3, 5, 7, 11 }
(iii) { January, June, July }
(iv) { a, e, i, o, u }
(v) { Tuesday, Thursday }
(vi) { 1, 4, 9, 16, 25 }
(vii) { 5, 10, 15, 20, 25, 30 }
Answer
(i) The elements 2, 4, 6, 8 and 10 are the even natural numbers less than 12.
{ 2, 4, 6, 8, 10 } = { x : x is an even natural number less than 12 }
(ii) The elements 2, 3, 5, 7 and 11 are the prime numbers less than 12.
{ 2, 3, 5, 7, 11 } = { x : x is a prime number less than 12 }
(iii) The elements January, June and July are the months whose names start with the letter J.
{ January, June, July } = { x : x is a month whose name starts with the letter J }
(iv) The elements a, e, i, o and u are the vowels in the English alphabet.
{ a, e, i, o, u } = { x : x is a vowel in the English alphabet }
(v) The elements Tuesday and Thursday are the days of the week whose names start with the letter T.
{ Tuesday, Thursday } = { x : x is a day of the week whose name starts with the letter T }
(vi) The elements 1, 4, 9, 16 and 25 are the perfect square natural numbers up to 25.
{ 1, 4, 9, 16, 25 } = { x : x is a perfect square natural number up to 25 }
(vii) The elements 5, 10, 15, 20, 25 and 30 are the natural numbers up to 30 that are divisible by 5.
{ 5, 10, 15, 20, 25, 30 } = { x : x is a natural number up to 30 and divisible by 5 }
Write each of the following sets in Roster (tabular) Form and also in Set-Builder Form:
(i) Set of all natural numbers that can divide 24 completely.
(ii) Set of odd numbers between 20 and 35.
(iii) Set of letters used in the word 'CALCUTTA'.
(iv) Set of names of the first five months of a year.
(v) Set of all two-digit numbers that are perfect squares as well.
Answer
(i) The natural numbers that divide 24 completely are 1, 2, 3, 4, 6, 8, 12 and 24.
Roster form: { 1, 2, 3, 4, 6, 8, 12, 24 }
Set-builder form: { x : x is a natural number which divides 24 completely }
(ii) The odd numbers between 20 and 35 are 21, 23, 25, 27, 29, 31 and 33.
Roster form: { 21, 23, 25, 27, 29, 31, 33 }
Set-builder form: { x : x is an odd number between 20 and 35 }
(iii) The letters in the word 'CALCUTTA' are C, A, L, C, U, T, T, A. Writing each letter only once, we get C, A, L, U, T.
Roster form: { c, a, l, u, t }
Set-builder form: { x : x is a letter used in the word 'CALCUTTA' }
(iv) The first five months of a year are January, February, March, April and May.
Roster form: { January, February, March, April, May }
Set-builder form: { x : x is the name of first five months of a year }
(v) The two-digit numbers that are perfect squares are 42 = 16, 52 = 25, 62 = 36, 72 = 49, 82 = 64 and 92 = 81.
Roster form: { 16, 25, 36, 49, 64, 81 }
Set-builder form: { x : x is a perfect square two-digit number }
Write, in Roster Form, the set of:
(i) the first four odd natural numbers each divisible by 5.
(ii) the counting numbers between 15 and 35; each of which is divisible by 6.
(iii) the names of the last three days of a week.
(iv) the names of the last four months of a year.
Answer
(i) The first four odd natural numbers each divisible by 5 are 5, 15, 25 and 35.
The required set = { 5, 15, 25, 35 }
(ii) The counting numbers between 15 and 35 which are divisible by 6 are 18, 24 and 30.
The required set = { 18, 24, 30 }
(iii) The last three days of a week are Friday, Saturday and Sunday.
The required set = { Friday, Saturday, Sunday }
(iv) The last four months of a year are September, October, November and December.
The required set = { September, October, November, December }