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Which of the ...

Question

Which of the following collections are sets?
(i) The collection of rich people in your district.
(ii) The collection of natural number less than 50.
(iii) the collection of most talented persons of India.
(iv) the collection of first ten prime integers.
(v) The collection of all days in a week starting with the letter 'T'
(vi) The collection of some months in a year.
(vii) the collection of all books in your school library.
(viii) the collection of smart boys in your class.
(ix) The collection of multiples of 7.
(x) The collection of students in your class who got a lot of marks in the first unit test.

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Solution

(i) The collection of rich people in a district is not a set, because it is not well defined.

(ii) The collection of natural numbers less than 50 is a set, because it is well defined. It includes 1, 2, 3, ... 49.

(iii) The collection of the most talented persons of India is not a set, because talent can be in any field. For instance, it can be a talent of dancing or singing. So, it is not well defined. Therefore, it is not a set.

(iv) The collection of the first ten prime integers includes 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. This is a collection of well defined elements. Therefore, it is a set.

(v) Collection of all days in a week starting with the letter 'T' includes {Tuesday, Thursday }.
It is well defined hence, it is a set .

(vi) Collection of some months in a year is not a set because here it is not defined which month we have to select .Therefore, it is not a set .

(vii) The collection of all books in a school library is a set because here it is well defined about the collection of all books of the school library.

(viii) The collection of smart boys in your class is not a set because smart can be in any sense. It is not well defined here.
Therefore, it is not a set .

(ix) Collection of multiples of 7 includes { 7,14,21,28....}. Because it is well defined, therefore, it is a set.

(x) The collection of students in a class who got a lot of marks in the first unit test is not a set because lot of marks can be any number .
It is not defined here. Therefore, it is not a set.

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