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.
Sets
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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.
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