Question

# Which of the following collections are sets ? Justify your answer : (i) A collection of all natural numbers less than 50. (ii) The collection of good hockey players in India. (iii) The collection of all girls in your class. (iv) The collection of most talented writers of India. (v) The collection of difficult topics in Mathematics. (vi) The collection of all months of a year beginning with the letter J. (vii) A collection of novels written by Munshi Prem Chand. (viii) The collection of all questions in this chapter. (ix) A collection of most dangerous animals of the world. (x) The collection of prime integers.

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Solution

## (i) The collection of all natural numbers less than 50 forms a set as it is well defined. (ii) It isnot a set as the term 'good' is not well defined. (iii) It forms a set as it is well defined. (iv) It is not a set as the term 'most' is not well defined. A writer may be talented in the eyw of on eperson, but he may not be talented in the eye of some other person. (v) It is not a set as the term 'difficult' is not well defined. A topic may be difficult for one person but may not be difficult for another person, so the term 'difficult' is vague. (vi) It forms a set as it is well defined. (vii) It forms a set as it is well defined. (viii) It forms a set as it is well defined. (ix) It is not a set as the term 'most dangerous' is not well defined. The notion of dangerous animals differs from person to person. (x) It forms a set as it is well defined.

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