alphabet is { a, e, i, o, u }. (c) The set of odd natural numbers is represented by { , , , . . .}.
The dots tell us that the list of odd numbers continue indefinitely. A 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.
In set-builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set. For example, in the set { a, e, i, o, u }, all the elements possess a common property, namely, each of them is a vowel in the English alphabet, and no other letter possess this property. Denoting this set by V, we write V = { x : x is a vowel in English alphabet} It may be observed that we describe the element of the set by using a symbol x (any other symbol like the letters y , z , etc. could be used) which is followed by a colon “ : ”.
After the sign of colon, we write the characteristic property possessed by the elements of the set and then enclose the whole description within braces. The above description of the set V is read as “the set of all x such that x is a vowel of the English alphabet”. In this description the braces stand for “the set of all”, the colon stands for “such that”. For example, the set A = { x : x is a natural number and < x < } is read as “the set of all x such that x is a natural number and x lies between and .” Hence, the numbers , , , , and are the elements of the set A.
If we denote the sets described in