Methods Of Describing A Set
Wednesday, January 5, 2011
The expression of sets has to be compact and clear otherwise the basic quality of the set being well-defined and distinactive is lost. Broadly there can be two approaches: (i) to the elements called the extension method, or (ii) toindicate the nature or characteristics and limits within which the elements lie. The latter method is rather unavoid able if the elements are too numerous, or not real butonly conceptual. These two approaches have been named variously as:
- Tabular, Roster Or Enumeration Method
- Selector, Property builder Or Rule Method
Tabular Method:
Under this method we enumerate or list all the elements of the set within brackes. However, there is no rigidity about these, use of even parentheses ( ) or brackers has been there in many books.
- A set of Vowels: A = { a, e, i, o, u }
- A set of odd natural numbers: N = { 1, 3, 5,.... }
- A Set of Prime Ministers: P = { Nehru, Indiara Gandhi, Obama, Bosh }
Selector Method:
Under this method the elements are not listed but are indicated by description of their characteristics. We may state some characteristics which an object must possess in order to be an element in the set.
Here we choose the letter x to represent an arbitrary element of the set and write.
- A= {x| x is a vowel in English alphabet}
- B= {x| x is an old natural number}
- C= {x| x is a Prime Minister of India}
- A= {x| x is a vowel in English alphabet}
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