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.

  1. A set of Vowels: A = { a, e, i, o, u }
  2. A set of odd natural numbers: N = { 1, 3, 5,.... }
  3. 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.

  1. A= {x| x is a vowel in English alphabet}
  2. B= {x| x is an old natural number}
  3. C= {x| x is a Prime Minister of India}
The vertical line “ | ” after x to be read as ‘such that’. Sometimes we use ‘:’ to denote ‘such that’, e.g.,
  • A= {x| x is a vowel in English alphabet}
It will be clear form the above that the toolbar method is particularly useful when the elements are few in number while the set-builder method is more suitable when the elements are numerous.


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