Mathematics
Write the following sets in tabular form:
(i) {x : x is a natural number and x < 7}
(ii) {x : x ∈ W and x ≤ 5}
(iii) {x : x is a month of a year having less than 31 days}
(iv) {x | x is a letter in the word 'CIRCUMFERENCE'}
(v) {x | x is a vowel in the word 'NOTATION'}
(vi) {x : x is a digit in the numeral 110526715}
(vii) {x : x is a factor of 48}
(viii) {x : x is a multiple of 11 and 0 ≤ x < 80}
(ix) {y : y is a two digit natural number divisible by 10}
Sets
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Answer
(i) The natural numbers less than 7 are 1, 2, 3, 4, 5 and 6.
{x : x is a natural number and x < 7} = {1, 2, 3, 4, 5, 6}
(ii) The whole numbers less than or equal to 5 are 0, 1, 2, 3, 4 and 5.
{x : x ∈ W and x ≤ 5} = {0, 1, 2, 3, 4, 5}
(iii) The months of a year having less than 31 days are February (28 or 29 days), April (30 days), June (30 days), September (30 days) and November (30 days).
{x : x is a month of a year having less than 31 days} = {February, April, June, September, November}
(iv) The letters in the word 'CIRCUMFERENCE' are C, I, R, C, U, M, F, E, R, E, N, C, E. Writing each letter only once, we get C, I, R, U, M, F, E, N.
{x | x is a letter in the word 'CIRCUMFERENCE'} = {C, I, R, U, M, F, E, N}
(v) The letters in the word 'NOTATION' are N, O, T, A, T, I, O, N. The vowels among these are O, A, I.
{x | x is a vowel in the word 'NOTATION'} = {O, A, I}
(vi) The digits in the numeral 110526715 are 1, 1, 0, 5, 2, 6, 7, 1, 5. Writing each digit only once, we get 1, 0, 5, 2, 6, 7.
{x : x is a digit in the numeral 110526715} = {1, 0, 5, 2, 6, 7}
(vii) The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
{x : x is a factor of 48} = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}
(viii) The multiples of 11 are 0, 11, 22, 33, 44, 55, 66, 77, 88, …… Out of these, those satisfying 0 ≤ x < 80 are 0, 11, 22, 33, 44, 55, 66 and 77.
{x : x is a multiple of 11 and 0 ≤ x < 80} = {0, 11, 22, 33, 44, 55, 66, 77}
(ix) The two digit natural numbers divisible by 10 are 10, 20, 30, 40, 50, 60, 70, 80 and 90.
{y : y is a two digit natural number divisible by 10} = {10, 20, 30, 40, 50, 60, 70, 80, 90}
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Related Questions
If V = {vowels in English alphabet}, write which of the following statements are true and which are false:
(i) c ∈ V
(ii) {a} ∈ V
(iii) a, e, i ∈ V
(iv) a, b ∈ V
(v) {a, u} ∉ V
(vi) {a, o, u} ∈ V
Write the following sets in roster form:
(i) the set of first five odd counting numbers
(ii) the set of all even natural numbers less than 101
(iii) {months of year whose names begin with a vowel}
(iv) {one digit natural numbers which are perfect squares}
(v) the set of multiples of 7 which lie between -20 and 25
(vi) {factors of 36}
(vii) {prime factors of 360}
(viii) the set of whole numbers which are multiples of 5
(ix) the set of all letters in the word 'CHENNAI'
(x) the set of all vowels in the word 'MUSSOORIE'
(xi) the set of all consonants in the word 'MATHEMATICS'
Write the following sets in roster form and also in set builder form:
(i) the set of integers which lie between -2 and 3 (both inclusive)
(ii) the set of letters in the word 'ULTIMATUM'
(iii) {months of a year whose names begin with J}
(iv) the set of single digit whole numbers which are perfect squares
State whether the following sets are empty, finite or infinite sets. In case of (non-empty) finite sets, mention the cardinal number.
(i) {all colours of a rainbow}
(ii) {x | x is a prime number between 7 and 11}
(iii) {x | x is a digit in the numeral 550131527}
(iv) {x | x is a letter in the word 'SUFFICIENT'}
(v) {x | x is a vowel in the word MATHEMATICS}
(vi) {x : x is an even whole number and x ≤ 20}
(vii) {x : x ∈ I and -2 ≤ x < 5}
(viii) {x : x is a prime number less than 25}
(ix) {x : x is a prime factor of 180}
(x) {x : x ∈ N and x is a composite number < 12}