Mathematics
State which of the following collections are sets:
(i) collection of odd natural numbers less than 50
(ii) collection of four colours of a rainbow
(iii) collection of first three days of a week
(iv) collection of all tall students of your class
(v) collection of all lovely flowers
(vi) collection of all rich people of Bengaluru
(vii) collection of some multiples of 5
(viii) collection of all even integers which lie between -5 and 15
(ix) collection of three youngest students of your class
(x) collection of three months of a year.
Sets
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Answer
(i) It is a set as it is well defined. The collection contains the odd natural numbers 1, 3, 5, 7, ……, 49.
(ii) It is not a set because it is not known which four colours of a rainbow are to be included in the collection.
(iii) It is a set as it is well defined. The collection contains the first three days of a week i.e. Sunday, Monday and Tuesday.
(iv) It is not a set because the given collection is not well defined—people may differ on whether a student of the class is tall or not.
(v) It is not a set because the given collection is not well defined—people may differ on whether a flower is lovely or not.
(vi) It is not a set because the given collection is not well defined—people may differ on whether a person of Bengaluru is rich or not.
(vii) It is not a set because it is not known which multiples of 5 are to be included in the collection.
(viii) It is a set as it is well defined. The collection contains the even integers -4, -2, 0, 2, 4, 6, 8, 10, 12, 14.
(ix) It is a set as it is well defined. The age of every student of the class can be determined and so the three youngest students of the class can be identified.
(x) It is not a set because it is not known which three months of a year are to be included in the collection.
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Related Questions
If E = {even integers}, then insert the appropriate symbol ∈ or ∉ in the blanks:
(i) 10 …. E
(ii) -8 …. E
(iii) 13 …. E
(iv) {6} …. E
(v) a …. E
(vi) -4, 12 …. E
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 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}