Mathematics
State which of the given collections are sets:
(i) collection of all poor people of Dhanbad
(ii) collection of all difficult problems in your maths book
(iii) collection of all popular cinema actors of India
(iv) collection of all countries of Asia
(v) collection of four countries of Asia
(vi) collection of three cities of India whose name start with the letter 'J'
(vii) collection of all people in this world over 50 years of age.
Answer
(i) It is not a set because the given collection is not well defined—people may differ on whether a person of Dhanbad is poor or not.
(ii) It is not a set because the given collection is not well defined—people may differ on whether a problem is difficult or not.
(iii) It is not a set because the given collection is not well defined—people may differ on whether a cinema actor is popular or not.
(iv) It is a set as it is well defined. The countries of Asia can be clearly listed.
(v) It is not a set because it is not known which four countries of Asia are to be included in the collection.
(vi) It is not a set because it is not known which three cities of India whose name start with 'J' are to be included in the collection (there are many such cities like Jaipur, Jodhpur, Jabalpur, Jaisalmer, etc.).
(vii) It is a set as it is well defined. The age of every person can be determined and thus people over 50 years can be clearly identified.
Related Questions
Statement I: An empty set is always a finite set but a finite set may or may not be empty.
Statement II: The cardinal number of a set of the English alphabet is less than 30.
Statement I is true but statement II is false.
Statement I is false but statement II is true.
Both Statement I and statement II are true.
Both Statement I and statement II are false.
Statement I: The cardinal number of the set A = {x | x ∈ N, x2 < 26} is 6.
Statement II: The number of different elements in a finite set is called its cardinal number.
Statement I is true but statement II is false.
Statement I is false but statement II is true.
Both Statement I and statement II are true.
Both Statement I and statement II are false.
If A = {3, 5, 7, 9, 11}, then write which of the following statements are true. If a statement is not true, mention why.
(i) 3 ∈ A
(ii) 5, 9 ∈ A
(iii) 8 ∉ A
(iv) 7 ∉ A
(v) {3} ∈ A
(vi) {5, 9} ∈ A
Write the following sets in the roster form:
(i) A = {x | x is a month of a year having 30 days}
(ii) B = {x | x = 2n, n ∈ W and n < 5}
(iii) C = {x | x ∈ N and x2 < 40}
(iv) D = {all letters in the word PERMISSION}
(v) E = {x : x ∈ I and x2 < 10}
(vi) F = {x : x ∈ N, 15 < x < 50 and x is divisible by 6}
(vii) the set of whole numbers which are greater than 14 and divisible by 7
(viii) the set of signs of four fundamental operations of arithmetic.