Thursday, June 3, 2010

Roster or tabular form

Let me explain about Roster or tabular form, one of the method of representing a set.
In roster form, all the elements of a set are listed, the elements are being separated
by commas and are enclosed within braces { }. For example, the set of all even
positive integers less than 7 is described in roster form as {2, 4, 6}. Some more
examples of representing a set in roster form are given below :

(a) The set of all natural numbers which divide 42 is {1, 2, 3, 6, 7, 14, 21, 42}.
Note : In roster form, the order in which the elements are listed is immaterial.
Thus, the above set can also be represented as {1, 3, 7, 21, 2, 6, 14, 42}.

(b) The set of all vowels in the English alphabet is {a, e, i, o, u}.

(c) The set of odd natural numbers is represented by {1, 3, 5, . . .}. The dots
tell us that the list of odd numbers continue indefinitely.
Note : It may be noted that while writing the set in roster form an element is not
generally repeated, i.e., all the elements are taken as distinct. For example, the set
of letters forming the word ‘SCHOOL’ is { S, C, H, O, L} or {H, O, L, C, S}. Here,
the order of listing elements has no relevance.
Hope the above explanation helped you, now let me explain you about Set-builder form.

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